"Let L be a tangent line to the parabola y2 = 4x $-$ 20 at (6, 2). If L is also a tangent to the ellipse ${{{x^2}} \over 2} + {{{y^2}} \over b} = 1$, then the value of b is equal to :"

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Accepted Answer

"Parabola y² = 4x $-$ 20

Tangent at P(6, 2) will be

$2y = 4\left( {{{x + 6} \over 2}} \right) - 20$

2y = 2x + 12 $-$ 20

2y = 2x $-$ 8

y = x $-$ 4

x $-$ y $-$ 4 = 0 ....... (1)

This is also tangent to ellipse ${{{x^2}} \over 2} + {{{y^2}} \over b} = 1$

Apply c² = a²m² + b²

($-$4)² = (2)(1) + b

b = 14"

Let L be a tangent line to the parabola y² = 4x $-$ 20 at (6, 2). If L is also a tangent to the ellipse ${{{x^2}} \over 2} + {{{y^2}} \over b} = 1$, then the value of b is equal to :

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Let L be a tangent line to the parabola y2 = 4x $-$ 20 at (6, 2). If L is also a tangent to the ellipse ${{{x^2}} \over 2} + {{{y^2}} \over b} = 1$, then the value of b is equal to :

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Let L be a tangent line to the parabola y² = 4x $-$ 20 at (6, 2). If L is also a tangent to the ellipse ${{{x^2}} \over 2} + {{{y^2}} \over b} = 1$, then the value of b is equal to :