Question

Let \( (x+\alpha)^{2}=-k(y+\beta) \) be the equation of the mirror image of the parabola \( y^{2}=16 x \) with respect to the line \( x+y+4=0 \), then the value of \( \frac{k}{2(\alpha+\beta)} \) is माना रेखा \( x + y +4=0 \) के सापेक्ष परवलय \( y ^{2}=16 x \) के दर्पण प्रतिबिम्ब का समीकरण \( (x+\alpha)^{2}=-k(y+\beta) \) है, तो \( \frac{ k }{2(\alpha+\beta)} \) का मान है

Answer 1

https://www.sarthaks.com/?qa=blob&qa_blobid=3222332854481285600

Let the general point on y²= 16x be A( t² , 4t ) 

Let B( h, k ) is the mirror image of A(t² , 4t ) with respect to line x + y + 4 = 0

Then B( h, k ) will be

Locus of B( h, k ) will be the equation of image Parabola of y² = 16x with respect to line x + y + 4 = 0