New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Ellipse question

2009 · Shift 1 · Q31

Guest · try one question or challengeGuest · try one question or challenge

PYQ Library
JEE Advanced
Mathematics
Ellipse
2009 · Shift 1 · Q31

Ellipse question

2009 · Shift 1 · Q31

JEE AdvancedMathematicsEllipseMultiple correct+4 / −2

In a triangle

ABC

with fixed base

BC

, the vertex

A

moves such that

\cos \,B + \cos \,C = 4{\sin ^2}{A \over 2}.

If

a, b

and

c

denote the lengths of the sides of the triangle opposite to the angles

A, B

and

C

, respectively, then

A
$b+c=4a$
B
$b+c=2a$
C
locus of point $A$ is an ellipse
D
locus of point $A$ is a pair of straight lines

More from Ellipse

The line passing through the extremity $A$ of the major axis and extremity $B$ of the minor axis of the ellipse $x^{2} + 9 y^{2} = 9$ meets its auxiliary circle at the point $M$ . Then the area of the triangle with vertices at $A$ , $M$ and…2009 · MCQ
The normal at a point $P$ on the ellipse $x^{2} + 4 y^{2} = 16$ meets the $x$ - axis $Q$ . If $M$ is the mid point of the line segment $P Q$ , then the locus of $M$ intersects the latus rectums of the given ellipse at the points2009 · MCQ
An ellipse intersects the hyperbola $2 x^{2} - 2 y^{2} = 1$ orthogonally. The eccentricity of the ellipse is reciprocal of that of the hyperbola. If the axes of the ellipse are along the coordinate axes then2009 · Multiple correct
Consider the two curves $C_{1} : y^{2} = 4 x, C_{2} : x^{2} + y^{2} - 6 x + 1 = 0$ . Then,2008 · MCQ
Let $P (x_{1}, y_{1})$ and $Q (x_{2}, y_{2}), y_{1} < 0, y_{2} < 0,$ be the end points of the latus rectum of the ellipse $x^{2} + 4 y^{2} = 4.$ The equations of parabolas with latus rectum $P Q$ are :2008 · Multiple correct
Let $P (x_{1}, y_{1})$ and $Q (x_{2}, y_{2})$ be two distinct points on the ellipse $\frac{x ^{2}}{9} + \frac{y ^{2}}{4} = 1$ such that $y_{1} > 0$ , and $y_{2} > 0$ . Let $C$ denote the circle $x^{2} + y^{2} = 9$ , and $M$ be the point $(3, 0)$ .…2025 · Multiple correct
Consider the ellipse $\frac{x ^{2}}{9} + \frac{y ^{2}}{4} = 1$ . Let $S (p, q)$ be a point in the first quadrant such that $\frac{p ^{2}}{9} + \frac{q ^{2}}{4} > 1$ . Two tangents are drawn from $S$ to the ellipse, of which one meets the ellipse at one end…2024 · MCQ
Let $T_{1}$ and $T_{2}$ be two distinct common tangents to the ellipse $E : \frac{x ^{2}}{6} + \frac{y ^{2}}{3} = 1$ and the parabola $P : y^{2} = 12 x$ . Suppose that the tangent $T_{1}$ touches $P$ and $E$ at the points $A_{1}$ and $A_{2}$ , respectively and the…2023 · Multiple correct