Suppose that the foci of the ellipse x 2 9 +   y 2 5 = 1 are f 1 ,   0   a n d   ( f 2 ,   0 ) where f 1 > 0   a n d   f 2 < 0 . Let P 1   a n d   P 2 be two parabolas with a common vertex at (0, 0) and with foci at f 1 ,   0 and 2 f 2 ,…

Question

Suppose that the foci of the ellipse x 2 9 + &#160; y 2 5 = 1 are f 1 , &#160; 0 &#160; a n d &#160; ( f 2 , &#160; 0 ) where f 1 &#62; 0 &#160; a n d &#160; f 2 &#60; 0 . Let P 1 &#160; a n d &#160; P 2 be two parabolas with a common vertex at (0, 0) and with foci at f 1 , &#160; 0 and 2 f 2 , &#160; 0 , respectively. Let T 1 be a tangent to P 1 which passes through 2 f 2 , &#160; 0 and T 2 be a tangent to P 2 which passes through ( f 1 , &#160; 0 ) . If m 1 is the slope of T 1 and m 2 is the slope of T 2 , then the value of 1 m 1 2 + &#160; m 2 2 is

Aicharya · Accepted Answer

f 1 ≡ ( 2 , 0 ) f 2 ≡ ( - 2 , 0 ) Parabolas are y 2 = 8 x y 2 = - 16 x T 1 : y = m x + 2 m 0 = - 4 m + 2 m ⇒ m 2 = 1 2 T 2 : y = m x - 4 m 2 m - 4 m = 0 ⇒ m 2 = 2 Now, m 2 2 + 1 m 1 2 = 2 + 2 = 4

Suppose that the foci of the ellipse x 2 9 +   y 2 5 = 1 are f 1 ,   0   a n d   ( f 2 ,…

Solution

Suppose that the foci of the ellipse x 2 9 + &#160; y 2 5 = 1 are f 1 , &#160; 0 &#160; a n d &#160; ( f 2 ,…

Solution

Suppose that the foci of the ellipse x 2 9 + y 2 5 = 1 are f 1 , 0 a n d ( f 2 ,…