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The curves $4 x^{2} + 9 y^{2} = 72 a n d x^{2} - y^{2} = 5 a t (3, 2)$

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touch each other

cut orthogonally

intersect at 450

intersect at600

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detailed solution

Correct option is B

4x2+9y2=72 Differentiating w .r.t. x, we have 8x+18ydydx=0⇒dydx=−49xyAt(3,2),dydx=−49×32=−23Also x2−y2=5⇒dydx=xyAt(3,2),dydx=32 Hence, the curves cut orthogonally .

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The curves 4x2+9y2=72 andx2−y2=5 at(3,2)

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The curves $4 x^{2} + 9 y^{2} = 72 a n d x^{2} - y^{2} = 5 a t (3, 2)$