The co-ordinate of a point on the auxiliary circle of the ellipse x2+2 y2=4 corresponding to the point on the ellipse whose eccentric angle is 60° will be

Question

The co-ordinate of a point on the auxiliary circle of the ellipse x2+2 y2=4 corresponding to the point on the ellipse whose eccentric angle is 60° will be (A) (√3, 1) (B) (1, √3) (C) (1,1) (D) (1,2)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/d5787ab834d3c1d36b7bfc5a159ea978-.png" /> (x2/4)+(y2/2)=1 Equation of auxiliary circle is x2+y2=4 ∴ Point on the auxiliary circle is p(2 cos 60°, 2 sin 60°) p(1, √3)

Q. The co-ordinate of a point on the auxiliary circle of the ellipse $x^{2} + 2 y^{2} = 4$ corresponding to the point on the ellipse whose eccentric angle is $6 0^{\circ}$ will be

$(3, 1)$

$(1, 3)$

$(1, 1)$

$(1, 2)$

$\frac{x ^{2}}{4} + \frac{y ^{2}}{2} = 1$
Equation of auxiliary circle is
$x^{2} + y^{2} = 4$
$∴$ Point on the auxiliary circle is
$p (2 cos 6 0^{\circ}, 2 sin 6 0^{\circ})$
$p (1, 3)$

Q. The co-ordinate of a point on the auxiliary circle of the ellipse x2+2y2=4 corresponding to the point on the ellipse whose eccentric angle is 60∘ will be

(3​,1)

(1,3​)

(1,1)

(1,2)