"If the points of intersections of the ellipse ${{{x^2}} \over {16}} + {{{y^2}} \over {{b^2}}} = 1$ and the circle x2 + y2 = 4b, b 4 lie on the curve y2 = 3x2, then b is equal to :"

Question

"If the points of intersections of the ellipse ${{{x^2}} \over {16}} + {{{y^2}} \over {{b^2}}} = 1$ and the circle x2 + y2 = 4b, b > 4 lie on the curve y2 = 3x2, then b is equal to :"

Accepted Answer

"${{{x^2}} \over {16}} + {{{y^2}} \over {{b^2}}} = 1$ ... (1)

${x^2} + {y^2} = 4b$ .... (2)

${y^2} = 3{x^2}$ .... (3)

From eq (2) and (3)

x² = b and y² = 3b

From equation (1)

${b \over {16}} + {{3b} \over {{b^2}}} = 1$

$\Rightarrow {b^2} + 48 = 16b$

$\Rightarrow b = 12$"

If the points of intersections of the ellipse ${{{x^2}} \over {16}} + {{{y^2}} \over {{b^2}}} = 1$ and the
circle x² + y² = 4b, b > 4 lie on the curve y² = 3x², then b is equal to :

Solution

About this question

Drill 25 more like these. Every day. Free.

If the points of intersections of the ellipse ${{{x^2}} \over {16}} + {{{y^2}} \over {{b^2}}} = 1$ and the circle x2 + y2 = 4b, b > 4 lie on the curve y2 = 3x2, then b is equal to :

Solution

About this question

More Conic Sections questions

Drill 25 more like these. Every day. Free.

If the points of intersections of the ellipse ${{{x^2}} \over {16}} + {{{y^2}} \over {{b^2}}} = 1$ and the
circle x² + y² = 4b, b > 4 lie on the curve y² = 3x², then b is equal to :