Identify the correct statement(s) -

Question

Identify the correct statement(s) - (A) the equation of the director circle of the ellipse, 5 x2+9 y2=45 is x2+y2=14. (B) the sum of the focal distances of the point (0,6) on the ellipse (x2/25)+(y2/36)=1 is 10 . (C) the point of intersection of any tangent to a parabola the perpendicular to it from the focus lies on directrix. (D) all of these

Tardigrade Admin · Accepted Answer

(1) Here (x2/9)+(y2/5)=1 ∴ director circle is (2) x 2+ y 2=9 Here b>a ∴ SP + S 1 P =2 b =12 (3) It is lies on tangent at vertex

Q. Identify the correct statement(s) -

the equation of the director circle of the ellipse, $5 x^{2} + 9 y^{2} = 45$ is $x^{2} + y^{2} = 14$ .

the sum of the focal distances of the point $(0, 6)$ on the ellipse $\frac{x ^{2}}{25} + \frac{y ^{2}}{36} = 1$ is 10 .

the point of intersection of any tangent to a parabola \& the perpendicular to it from the focus lies on directrix.

all of these

(1) Here $\frac{x ^{2}}{9} + \frac{y ^{2}}{5} = 1$
$∴$ director circle is
(2) $x^{2} + y^{2} = 9$ Here $b > a$
$∴ SP + S_{1} P = 2 b = 12$
(3) It is lies on tangent at vertex

Q. Identify the correct statement(s) -

the equation of the director circle of the ellipse, 5x2+9y2=45 is x2+y2=14.

the sum of the focal distances of the point (0,6) on the ellipse 25x2​+36y2​=1 is 10 .

the point of intersection of any tangent to a parabola \& the perpendicular to it from the focus lies on directrix.

all of these

(1) Here 9x2​+5y2​=1 ∴ director circle is (2) x2+y2=9 Here b>a ∴SP+S1​P=2b=12 (3) It is lies on tangent at vertex

the equation of the director circle of the ellipse, $5 x^{2} + 9 y^{2} = 45$ is $x^{2} + y^{2} = 14$ .

the sum of the focal distances of the point $(0, 6)$ on the ellipse $\frac{x ^{2}}{25} + \frac{y ^{2}}{36} = 1$ is 10 .

(1) Here $\frac{x ^{2}}{9} + \frac{y ^{2}}{5} = 1$
$∴$ director circle is
(2) $x^{2} + y^{2} = 9$ Here $b > a$
$∴ SP + S_{1} P = 2 b = 12$
(3) It is lies on tangent at vertex