Straight Lines and Pair of Straight Lines PYQs - Last 10 Years

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Last 10 Years Straight Lines and Pair of Straight Lines Questions

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1Straight Lines And Pair Of Straight Lines

The distance of a point \((2,5)\) from the line \(3 x+y+4=0\) measured along the line \(L_1\) and \(L_1\) are same. If slope of line \(L_1\) is \(\frac{3}{4}\), then slope of the line \(\mathrm{L}_2\) is

2Straight Lines And Pair Of Straight Lines

If the distance between the parallel lines given by the equation \(x^2+4 x y+p y^2+3 x+q y-4=0\) is \(\lambda\), then \(\lambda^2=\)

3Straight Lines And Pair Of Straight Lines

The equation of a line, whose perpendicular distance from the origin is 7 units and the angle, which the perpendicular to the line from the origin makes, is \(120^{\circ}\) with positive \(\mathrm{X}\)-axis, is

4Straight Lines And Pair Of Straight Lines

If the slope of one of the lines represented by \(a x^2+(2 a+1) x y+2 y^2=0\) is reciprocal of the slope of the other, then the sum of squares of slopes is

5Straight Lines And Pair Of Straight Lines

The perpendiculars are drawn to lines \(L_1\) and \(L_2\) from the origin making an angle \(\frac{\pi}{4}\) and \(\frac{3 \pi}{4}\) respectively with positive direction of \(\mathrm{X}\)-axis. If both the lines are at unit distance from the...

6Straight Lines And Pair Of Straight Lines

\(\mathrm{p}\) is the length of perpendicular from the origin to the line whose intercepts on the axes are a and \(\mathrm{b}\) respectively, then \(\frac{1}{\mathrm{a}^2}+\frac{1}{\mathrm{~b}^2}\) equals

7Straight Lines And Pair Of Straight Lines

The centroid of the triangle formed by the lines \(x+3 y=10\) and \(6 x^2+x y-y^2=0\) is

8Straight Lines And Pair Of Straight Lines

Let \(P \equiv(-3,0), Q \equiv(0,0)\) and \(R \equiv(3,3 \sqrt{3})\) be three points. Then the equation of the bisector of the angle \(\mathrm{PQR}\) is

9Straight Lines And Pair Of Straight Lines

A line is drawn through the point \((1,2)\) to meet the co-ordinate axes at \(\mathrm{P}\) and \(\mathrm{Q}\) such that it forms a \(\triangle \mathrm{OPQ}\), where \(\mathrm{O}\) is the origin. If the area of \(\triangle \mathrm{OPQ}\) is ...

10Straight Lines And Pair Of Straight Lines

The base of an equilateral triangle is represented by the equation \(2 x-y-1=0\) and its vertex is \((1,2)\), then the length (in units) of the side of the triangle is

11Straight Lines And Pair Of Straight Lines

If the angle between the lines given by \(x^2-3 x y+\lambda y^2+3 x-5 y+2=0 ; \lambda \geq 0\) is \(\tan ^{-1}\left(\frac{1}{3}\right)\), then the value of \(\lambda\) is

12Straight Lines And Pair Of Straight Lines

\(P S\) is the median of the triangle with vertices at \(P(2,2), Q(6,-1)\) and \(R(7,3)\), then the intercepts on the coordinate axes of the line passing through point \((1,-1)\) and parallel to PS are respectively

13Straight Lines And Pair Of Straight Lines

Let \(P Q R\) be a right angled isosceles triangle, right angled at \(Q(2,1)\). If the equation of the line \(P R\) is \(2 x+y=3\), then the combined equation representing the pair of lines \(P Q\) and \(Q R\) is

14Straight Lines And Pair Of Straight Lines

Let \(\mathrm{PQR}\) be a right angled isosceles triangle, right angled at \(\mathrm{P}(2,1)\). If the equation of the line \(\mathrm{QR}\) is \(2 x+y=3\), then the equation representing the pair of lines \(P Q\) and \(P R\) is

15Straight Lines And Pair Of Straight Lines

The co-ordinates of the points on the line \(2 x-y=5\) which are the distance of 1 unit from the line \(3 x+4 y=5\) are

16Straight Lines And Pair Of Straight Lines

If \(\mathrm{k}_{\mathrm{i}}\) are possible values of \(\mathrm{k}\) for which lines \(\mathrm{k} x+2 y+2=0,2 x+\mathrm{k} y+3=0\) and \(3 x+3 y+\mathrm{k}=0\) are concurrent, then \(\sum \mathrm{k}_{\mathrm{i}}\) has the value

17Straight Lines And Pair Of Straight Lines

If the pair of lines given by \((x \cos \alpha+y \sin \alpha)^2=\left(x^2+y^2\right) \sin ^2 \alpha\) are perpendicular to each other, then \(\alpha\) is

18Straight Lines And Pair Of Straight Lines

\(\mathrm{a}\) and \(\mathrm{b}\) are the intercepts made by a line on the co-ordinate axes. If \(3 \mathrm{a}=\mathrm{b}\) and the line passes through \((1,3)\), then the equation of the line is

19Straight Lines And Pair Of Straight Lines

If the angle between the lines represented by the equation \(x^2+\lambda x y-y^2 \tan ^2 \theta=0\) is \(2 \theta\), then the value of \(\lambda\) is

20Straight Lines And Pair Of Straight Lines

The joint equation of the lines pair of lines passing through the point \((3,-2)\) and perpendicular to the lines \(5 x^2+2 x y-3 y^2=0\) is

21Straight Lines And Pair Of Straight Lines

The points \((1,3),(5,1)\) are opposite vertices of a diagonal of a rectangle. If the other two vertices lie on the line \(y=2 x+\mathrm{c}\), then one of the vertex on the other diagonal is

22Straight Lines And Pair Of Straight Lines

The number of integral values of \(\mathrm{p}\) in the domain \([-5,5]\), such that the equation \(2 x^2+4 x y-p y^2+4 x+q y+1=0\) represents pair of lines, are

23Straight Lines And Pair Of Straight Lines

Two sides of a square are along the lines \(5 x-12 y+39=0\) and \(5 x-12 y+78=0\), then area of the square is

24Straight Lines And Pair Of Straight Lines

The joint equation of a pair of lines passing through the origin and making an angle of \(\frac{\pi}{4}\) with the line \(3 x+2 y-8=0\) is

25Straight Lines And Pair Of Straight Lines

The equations of the lines passing through the point \((3,2)\) and making an acute angle of \(45^{\circ}\) with the line \(x-2 y-3=0\) are

26Straight Lines And Pair Of Straight Lines

The joint equation of pair of lines through the origin and making an equilateral triangle with the line \(y = 5\) is

27Straight Lines And Pair Of Straight Lines

If the lines respresented by \(a x^2-b x y-y^2=0\) make angle \(\alpha\) and \(\beta\) with the positive direction of \(\mathrm{X}\)-axis, then \(\tan (\alpha+\beta)=\)

28Straight Lines And Pair Of Straight Lines

If the angle between the lines is \(\frac{\pi^{\mathrm{C}}}{4}\) and slope of one of the lines is \(\frac{1}{2}\), then slope of the other line is

29Straight Lines And Pair Of Straight Lines

If one of the lines given by \(k x^2+x y-y^2=0\) bisect the angle between the co-ordinate axes then the values of \(k\) are

30Straight Lines And Pair Of Straight Lines

The equation of a line with slope \(-\frac{1}{\sqrt{2}}\) and makes an intercept of \(2 \sqrt{2}\) units on negative direction of \(y\)-axis is

31Straight Lines And Pair Of Straight Lines

If the lines represented by \((k^2+2) x^2+3 x y-6 y^2=0\) are perpendicular to each other, then the values of \(\mathrm{K}\) are

32Straight Lines And Pair Of Straight Lines

The acute angle between the lines \(\left(x^2+y^2\right) \sin \theta+2 x y=0\) is

33Straight Lines And Pair Of Straight Lines

If the polar co-ordinates of a point are \(\left(2, \frac{\pi^{\mathrm{c}}}{4}\right)\), then its Cartesian co-ordinates are

34Straight Lines And Pair Of Straight Lines

The equation of line, where length of the perpendicular segment from origin to the line is 4 and the inclination of this perpendicular segment with the positive direction of X-axis is 30\(^\circ\), is

35Straight Lines And Pair Of Straight Lines

The combined equation of a pair of lines passing through the origin and inclined at \(60^{\circ}\) and \(30=\) respectively with \(x\)-axis is

36Straight Lines And Pair Of Straight Lines

If two lines represented by \(a x^2+2 h x y+b y^2=0\) makes angles \(\alpha\) and \(\beta\) with positive direction of \(\mathrm{X}\)-axis, then \(\tan (\alpha+\beta)=\)

37Straight Lines And Pair Of Straight Lines

If the slopes of the lines given by the equation \(a x^2+2 h x y+b y^2=0\) are in the ratio \(5: 3\), then the ratio \(h^2: a b=\)

38Straight Lines And Pair Of Straight Lines

The distance between the lines \(3 x+4 y=9\) and \(6 x+8 y=15\) is

39Straight Lines And Pair Of Straight Lines

If \(4 a b=3 h^2\), then the ratio of slopes of the lines represented by \(a x^2+2 h x y+b y^2=0\) is

40Straight Lines And Pair Of Straight Lines

The joint equation of pair of lines through the origin and having slopes \((1+\sqrt{2})\) and \(\frac{1}{(1+\sqrt{2})}\) is

41Straight Lines And Pair Of Straight Lines

The equation of perpendicular bisector of the line segment joining \(A(-2,3)\) and \(B(6,-5)\) is

42Straight Lines And Pair Of Straight Lines

Area of the triangle formed by the lines \(y^2-9 x y+18 x^2=0\) and \(y=9\) is

43Straight Lines And Pair Of Straight Lines

If slope of one of the lines ax\(^2\) + 2hxy + by\(^2\) = 0 is twice that of the other, then h\(^2\) : ab is

44Straight Lines And Pair Of Straight Lines

If the line joining two points \(\mathrm{A}(2,0)\) and \(\mathrm{B}(3,1)\) is rotated about \(\mathrm{A}\) in anticlockwise direction through an angle of \(15^{\circ}\), then the equation of the line in new position is

45Straight Lines And Pair Of Straight Lines

If the sum of slopes of lines represented by \(\mathrm{ax^2+8xy+5y^2=0}\) is twice their product, then a =

46Straight Lines And Pair Of Straight Lines

If lines represented by the equation \(\mathrm{px}^2-\mathrm{qy^{2 }}=0\) are distinct, then

47Straight Lines And Pair Of Straight Lines

The product of the perpendicular distances from \((2,-1)\) to the pair of lines \(2 x^2-5 x y+2 y^2=0\) is

48Straight Lines And Pair Of Straight Lines

The equation of a line passing through \((\mathrm{p} \cos \propto, \mathrm{p} \sin \propto)\) ) and making an angle \((90+\propto)\) with positive direction of \(\mathrm{X}\)-axis is

49Straight Lines And Pair Of Straight Lines

If the polar co-ordinates of a point are \(\left(\sqrt{2}, \frac{\pi}{4}\right)\), then its Cartesian co-ordinates are

50Straight Lines And Pair Of Straight Lines

If the two lines given by \(a x^2+2 h x y+b y^2=0\) make inclinations \(\propto\) and \(\beta\), then \(\tan (\alpha+\beta)=\)