New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Ellipse question

2023 · Shift 1 · Q19

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

PYQ Library
JEE Advanced
Mathematics
Ellipse
2023 · Shift 1 · Q19

Ellipse question

2023 · Shift 1 · Q19

JEE AdvancedMathematicsEllipseMultiple correct+4 / −2

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 tangent

T_2

touches

P

and

E

at the points

A_4

and

A_3

, respectively. Then which of the following statements is(are) true?

A
The area of the quadrilateral $A_1 A_2 A_3 A_4$ is 35 square units
B
The area of the quadrilateral $A_1 A_2 A_3 A_4$ is 36 square units
C
The tangents $T_1$ and $T_2$ meet the $x$ -axis at the point $(-3,0)$
D
The tangents $T_1$ and $T_2$ meet the $x$ -axis at the point $(-6,0)$

More from Ellipse

Consider the ellipse $\frac{x ^{2}}{4} + \frac{y ^{2}}{3} = 1$ Let $H (α, 0), 0 < α < 2$ , be a point. A straight line drawn through $H$ parallel to the $y$ -axis crosses the ellipse and its auxiliary circle at points $E$ and $F$ … Includes table2022 · MCQ
Let E be the ellipse $\frac{x ^{2}}{16} + \frac{y ^{2}}{9} = 1$ . For any three distinct points P, Q and Q' on E, let M(P, Q) be the mid-point of the line segment joining P and Q, and M(P, Q') be the mid-point of the line segment…2021 · Numerical
Define the collections {E1, E2, E3, ...} of ellipses and {R1, R2, R3.....} of rectangles as follows : $E_{1} : \frac{x ^{2}}{9} + \frac{y ^{2}}{4} = 1$ R1 : rectangle of largest area, with sides parallel to the axes, inscribed in E1; En :…2019 · Multiple correct
Let S be the circle in the XY-plane defined the equation x2 + y2 = 4. Let P be a point on the circle S with both coordinates being positive. Let the tangent to S at P intersect the coordinate axes at the points M and N. Then, the mid-point…2018 · MCQ
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…2018 · Multiple correct
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