16:I[8216,["972","static/chunks/972-b28da0de92681928.js","47","static/chunks/47-a7f06e9eda1ac756.js","115","static/chunks/app/%5Bexam%5D/questions/%5Byear%5D/%5Bsubject%5D/%5Bchapter%5D/%5BquestionId%5D/page-7b6f0a12b9cc0206.js"],"BackButton"] 17:I[1553,["972","static/chunks/972-b28da0de92681928.js","47","static/chunks/47-a7f06e9eda1ac756.js","115","static/chunks/app/%5Bexam%5D/questions/%5Byear%5D/%5Bsubject%5D/%5Bchapter%5D/%5BquestionId%5D/page-7b6f0a12b9cc0206.js"],"QuestionViewer"] 15:T4d9,{"@context":"https://schema.org","@type":"Quiz","name":"Ap Eapcet 2024 Circle PYQ with Solution","url":"https://pyq-test-series-platform-alsjdcxu2-sameers-projects-41c5a71e.vercel.app/ap-eapcet/questions/2024/mathematics/circle/m8h1f6l1","educationalLevel":"Entrance exam preparation","about":"Ap Eapcet / Mathematics / Circle","hasPart":{"@type":"Question","name":"Ap Eapcet 2024 Circle PYQ with Solution","text":"If power of a point (4,2) with respect to the circle x^2+y^2-2 \\alpha x+6 y+\\alpha^2-16=0 is 9 , then the sum of the lengths of all possible intercepts made by such circles on the coordinate axes is","eduQuestionType":"mcq","acceptedAnswer":{"@type":"Answer","text":"A"},"comment":{"@type":"Comment","text":"The power of the point (4, 2) with respect to the given circle is 9. To find the circle's equation, use the power of the point: 16 + 4 - 8\\alpha + 12 + \\alpha^2 - 16 = 9 Solving this equation gives: \\alpha^2 - 8\\alpha + 7 = 0 which results in: \\alpha = 1 \\quad \\text{or} \\quad \\alpha = 7 Thus, the possible equations of the circles are: x^2 + y^2 - 2x + 6y - 15 = 0 x^2 + y^2 - 14x + 6y + 33 = 0 For the equation x^2 + y^2 - 2x + 6y - 15 = 0: Length of intercepts on the X-axis : 2\\sqrt{g^2 - c} = 2..."}}}18:T4f5,

The power of the point $(4, 2)$ with respect to the given circle is 9.

To find the circle's equation, use the power of the point:

$ 16 + 4 - 8\alpha + 12 + \alpha^2 - 16 = 9 $

Solving this equation gives:

$ \alpha^2 - 8\alpha + 7 = 0 $

which results in:

Circle

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