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:T468,{"@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/m9yadxiz","educationalLevel":"Entrance exam preparation","about":"Ap Eapcet / Mathematics / Hyperbola","hasPart":{"@type":"Question","name":"Ap Eapcet 2024 Hyperbola PYQ with Solution","text":"The line 21 x+5 y=k touches the hyperbola 7 x^2-5 y^2=232, then k is equal to","eduQuestionType":"mcq","acceptedAnswer":{"@type":"Answer","text":"A"},"comment":{"@type":"Comment","text":"To determine the value of k for which the line 21x + 5y = k is tangent to the hyperbola 7x^2 - 5y^2 = 232 , we apply the condition for tangency of a line to a hyperbola. Tangency Condition: For a line y = mx + c to be tangent to the hyperbola \\frac{x^2}{a^2} - \\frac{y^2}{b^2} = 1, the condition is c^2 = a^2 m^2 - b^2 . Given: The line equation is: y = \\frac{-21}{5}x + \\frac{k}{5} Hence, m = \\frac{-21}{5} and c = \\frac{k}{5} . The hyperbola 7x^2 - 5y^2 = 232 can be written as: \\frac{x^2}{\\frac{2..."}}}18:T53d,

To determine the value of $ k $ for which the line $ 21x + 5y = k $ is tangent to the hyperbola $ 7x^2 - 5y^2 = 232 $, we apply the condition for tangency of a line to a hyperbola.

Tangency Condition:

For a line $ y = mx + c $ to be tangent to the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$, the condition is $ c^2 = a^2 m^2 - b^2 $.

Given:

The line equation is:

Hyperbola

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