New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Ellipse question

2018 · Shift 2 · Q22

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

PYQ Library
JEE Advanced
Mathematics
Ellipse
2018 · Shift 2 · Q22

Ellipse question

2018 · Shift 2 · Q22

JEE AdvancedMathematicsEllipseMultiple correct+4 / −1

Consider two straight lines, each of which is tangent to both the circle x2 + y2 = (1/2) and the parabola y2 = 4x. Let these lines intersect at the point Q. Consider the ellipse whose centre is at the origin O(0, 0) and whose semi-major axis is OQ. If the length of the minor axis of this ellipse is

\sqrt 2

, then which of the following statement(s) is (are) TRUE?

A
For the ellipse, the eccentricity is 1 $\sqrt 2$ and the length of the latus rectum is 1
B
For the ellipse, the eccentricity is 1/2 and the length of the latus rectum is 1/2
C
The area of the region bounded by the ellipse between the lines $x = {1 \over {\sqrt 2 }}$ and x = 1 is ${1 \over {4\sqrt 2 }}(\pi - 2)$
D
The area of the region bounded by the ellipse between the lines $x = {1 \over {\sqrt 2 }}$ and x = 1 is ${1 \over {16}}(\pi - 2)$

More from Ellipse

For how many values of p, the circle x2 + y2 + 2x + 4y $-$ p = 0 and the coordinate axes have exactly three common points?2017 · Numerical
Let $F_{1} (x_{1}, 0)$ and $F_{2} (x_{2}, 0)$ for $x_{1} < 0$ and $x_{2} > 0$ , be the foci of the ellipse $\frac{x ^{2}}{9} + \frac{y ^{2}}{8} = 1$ . Suppose a parabola having vertex at the origin and…2016 · MCQ
Let $F_{1} (x_{1}, 0)$ and $F_{2} (x_{2}, 0)$ for $x_{1} < 0$ and $x_{2} > 0$ , be the foci of the ellipse $\frac{x ^{2}}{9} + \frac{y ^{2}}{8} = 1$ . Suppose a parabola having vertex at the origin and…2016 · MCQ
Let $E_{1}$ and $E_{2}$ be two ellipses whose centres are at the origin. The major axes of $E_{1}$ and $E_{2}$ lie along the $x$ -axis and the $y$ -axis, respectively. Let $S$ be the circle $x^{2} + (y - 1)^{2} = 2$ . The…2015 · Multiple correct
The common tangents to the circle $x^{2} + y^{2} = 2$ and the parabola $y^{2} = 8 x$ touch the circle at the points $P, Q$ and the parabola at the points $R$ , $S$ . Then the area of the quadrilateral $P QR S$ is2014 · MCQ
A vertical line passing through the point $\frac{x ^{2}}{4} + \frac{y ^{2}}{3} = 1$ intersects the ellipse $\frac{x ^{2}}{4} + \frac{y ^{2}}{3} = 1$ at the points $P$ and $Q$ . Let the tangents to the ellipse at $P$ and $Q$ meet at the point $R$ . If $Δ (h)$ …2013 · Numerical
The ellipse $E_{1} : \frac{x ^{2}}{9} + \frac{y ^{2}}{4} = 1$ is inscribed in a rectangle $R$ whose sides are parallel to the coordinate axes. Another ellipse $E_{2}$ passing through the point $R$ circumscribes the rectangle $R$ . The…2012 · MCQ
Tangents are drawn from the point $P (3, 4)$ to the ellipse $\frac{x ^{2}}{9} + \frac{y ^{2}}{4} = 1$ touching the ellipse at points $A$ and $B$ . The coordinates of $A$ and $B$ are2010 · MCQ