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:T472,{"@context":"https://schema.org","@type":"Quiz","name":"Ap Eapcet 2024 Hyperbola PYQ with Solution","url":"https://pyq-test-series-platform-alsjdcxu2-sameers-projects-41c5a71e.vercel.app/ap-eapcet/questions/2024/mathematics/hyperbola/m9s6vdyd","educationalLevel":"Entrance exam preparation","about":"Ap Eapcet / Mathematics / Hyperbola","hasPart":{"@type":"Question","name":"Ap Eapcet 2024 Hyperbola PYQ with Solution","text":"The transformed equation of x^2-y^2+2 x+4 y=0 when the origin is shifted to the point (-1,2) is","eduQuestionType":"mcq","acceptedAnswer":{"@type":"Answer","text":"C"},"comment":{"@type":"Comment","text":"To transform the equation x^2 - y^2 + 2x + 4y = 0 when the origin is shifted to the point (-1, 2), we proceed as follows: Given equation : x^2 - y^2 + 2x + 4y = 0 New origin : (h, k) = (-1, 2) Transform the variables : Let X = x - h and Y = y - k . So, X = x - (-1) = x + 1 Y = y - 2 Solving for x and y : x = X - 1 y = Y + 2 Now, substituting these into the given equation: (x - 1)^2 - (y + 2)^2 + 2(x - 1) + 4(y + 2) = 0 Expanding each term: (x - 1)^2 = x^2 - 2x + 1 (y + 2)^2 = y^2 + 4y + 4 Subst..."}}}18:T422,

To transform the equation $x^2 - y^2 + 2x + 4y = 0$ when the origin is shifted to the point $(-1, 2)$, we proceed as follows:

Given equation:

$ x^2 - y^2 + 2x + 4y = 0 $

New origin:

$ (h, k) = (-1, 2) $

Transform the variables:

Let $ X = x - h $ and $ Y = y - k $.

So,

$ X = x - (-1) = x +

Hyperbola

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