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Question: If curves \(\frac{x^{2}}{a^{2}}\)+ \(\frac{y^{2}}{b^{2}}\) = 1 and \(\frac{x^{2}}{\mathcal{l}^{2}}\)...

If curves x2a2\frac{x^{2}}{a^{2}}+ y2b2\frac{y^{2}}{b^{2}} = 1 and x2l2\frac{x^{2}}{\mathcal{l}^{2}} – y2m2\frac{y^{2}}{m^{2}} = 1 intersect

orthogonal then –

A

a2 + b2 = l2 + m2

B

a2 – b2= l2 – m2

C

a2 – b2= l2 + m2

D

a2 + b2= l2 – m2

Answer

a2 – b2= l2 + m2

Explanation

Solution

m1. m2 = –1 .......(i)

and x2a2\frac{x^{2}}{a^{2}}+ y2b2\frac{y^{2}}{b^{2}} = x2l2\frac{x^{2}}{\mathcal{l}^{2}} – x2m2\frac{x^{2}}{m^{2}} .......(ii)

Now compare x2y2\frac{x^{2}}{y^{2}} from both the equation.