1
JEE Advanced 2021 Paper 2 Online
Numerical
+4
-0
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 _______.
2
JEE Advanced 2017 Paper 1 Offline
Numerical
+3
-0
For how many values of p, the circle x2 + y2 + 2x + 4y $$-$$ p = 0 and the coordinate axes have exactly three common points?
3
JEE Advanced 2013 Paper 1 Offline
Numerical
+4
-0
A vertical line passing through the point $$(h,0)$$ intersects the ellipse $${{{x^2}} \over 4} + {{{y^2}} \over 3} = 1$$ at the points $$P$$ and $$Q$$. Let the tangents to the ellipse at $$P$$ and $$Q$$ meet at the point $$R$$. If $$\Delta \left( h \right)$$$$=$$ area of the triangle $$PQR$$, $${{\Delta _1}}$$ $$= \mathop {\max }\limits_{1/2 \le h \le 1} \Delta \left( h \right)$$ and $${{\Delta _2}}$$ $$= \mathop {\min }\limits_{1/2 \le h \le 1} \Delta \left( h \right)$$, then $${8 \over {\sqrt 5 }}{\Delta _1} - 8{\Delta _2} =$$