New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Ellipse question

2021 · Shift 2 · Q37

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

PYQ Library
JEE Advanced
Mathematics
Ellipse
2021 · Shift 2 · Q37

Ellipse question

2021 · Shift 2 · Q37

JEE AdvancedMathematicsEllipseNumerical+4 / −1

Let E be the ellipse

{{{x^2}} \over {16}} + {{{y^2}} \over 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 joining P and Q'. Then the maximum possible value of the distance between M(P, Q) and M(P, Q'), as P, Q and Q' vary on E, is

\underline{\hspace{2cm}}

.

Numerical answer

More from Ellipse

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
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