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:T49d,{"@context":"https://schema.org","@type":"Quiz","name":"Viteee 2024 Differentiation PYQ with Solution","url":"https://pyq-test-series-platform-alsjdcxu2-sameers-projects-41c5a71e.vercel.app/viteee/questions/2024/mathematics/differentiation/m9bd62jw","educationalLevel":"Entrance exam preparation","about":"Viteee / Mathematics / Differentiation","hasPart":{"@type":"Question","name":"Viteee 2024 Differentiation PYQ with Solution","text":"If the curves \\frac{x^2}{a}+\\frac{y^2}{4}=1 and y^3=16 x intersect at right angles, then ' a ' equals to","eduQuestionType":"mcq","acceptedAnswer":{"@type":"Answer","text":"C"},"comment":{"@type":"Comment","text":"To determine the value of a when the curves \\frac{x^2}{a} + \\frac{y^2}{4} = 1 and y^3 = 16x intersect at right angles, we follow these steps: Differentiate Both Curves : For the ellipse \\frac{x^2}{a} + \\frac{y^2}{4} = 1: \\frac{2x}{a} + \\frac{2y}{4} \\cdot \\frac{dy}{dx} = 0 \\implies \\frac{dy}{dx} = -\\frac{4x}{ay} \\quad \\text{(i)} For the curve y^3 = 16x: 3y^2 \\cdot \\frac{dy}{dx} = 16 \\implies \\frac{dy}{dx} = \\frac{16}{3y^2} \\quad \\text{(ii)} Apply the Orthogonality Condition : The curves intersec..."}}}18:T49f,

To determine the value of $ a $ when the curves $\frac{x^2}{a} + \frac{y^2}{4} = 1$ and $y^3 = 16x$ intersect at right angles, we follow these steps:

Differentiate Both Curves:

For the ellipse $\frac{x^2}{a} + \frac{y^2}{4} = 1$:

$ \frac{2x}{a} + \frac{2y}{4} \cdot \frac{dy}{dx} = 0 \implies \frac{dy}{dx}

Differentiation

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