If vertices of the ellipse 9 x2+25 y2-18 x+100 y-116=0 are the extremities of latus rectum of a parabola whose vertex is (x1, y1) where y1-2, then

Question

If vertices of the ellipse 9 x2+25 y2-18 x+100 y-116=0 are the extremities of latus rectum of a parabola whose vertex is (x1, y1) where y1>-2, then (A) length of latus rectum of the ellipse is (50/3). (B) directrix of the parabola is y-3=0. (C) smaller area enclosed by the parabola and the ellipse is (5/6)(9 π-20) sq. units. (D) smaller area enclosed by the parabola and the ellipse is (5/6)(9 π-10) sq. units.

Tardigrade Admin · Accepted Answer

Correct answer is (b) directrix of the parabola is y-3=0.Correct answer is (c) smaller area enclosed by the parabola and the ellipse is (5/6)(9 π-20) sq. units.

Q. If vertices of the ellipse $9 x^{2} + 25 y^{2} - 18 x + 100 y - 116 = 0$ are the extremities of latus rectum of a parabola whose vertex is $(x_{1}, y_{1})$ where $y_{1} > - 2$ , then

length of latus rectum of the ellipse is $\frac{50}{3}$ .

directrix of the parabola is $y - 3 = 0$ .

smaller area enclosed by the parabola and the ellipse is $\frac{5}{6} (9 π - 20)$ sq. units.

smaller area enclosed by the parabola and the ellipse is $\frac{5}{6} (9 π - 10)$ sq. units.

Correct answer is (b) directrix of the parabola is $y - 3 = 0$ . Correct answer is (c) smaller area enclosed by the parabola and the ellipse is $\frac{5}{6} (9 π - 20)$ sq. units.

Q. If vertices of the ellipse 9x2+25y2−18x+100y−116=0 are the extremities of latus rectum of a parabola whose vertex is (x1​,y1​) where y1​>−2, then

length of latus rectum of the ellipse is 350​.

directrix of the parabola is y−3=0.

smaller area enclosed by the parabola and the ellipse is 65​(9π−20) sq. units.

smaller area enclosed by the parabola and the ellipse is 65​(9π−10) sq. units.