JEE Main 2021 — Mathematics Coordinate Geometry
A ray of light through (2,1) is reflected at a point P on the y− axis and then passes through the point (5,3). If this reflected ray is the directrix of an ellipse with eccentricity 31 and the distance of the nearer focus from this directrix is 538, then the equation of the other directrix can be:
Held on 27 Jul 2021 · Verified 6 Jul 2026.
11x+7y+8=0 or 11x+7y−15=0
11x−7y−8=0 or 11x+7y+15=0
2x−7y+29=0 or 2x−7y−7=0
2x−7y−39=0 or 2x−7y−7=0
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Let the image of parabola $x^{2}=4 y$, in the line $x-y=1$ be $(y+a)^{2}=b(x-c)$, $a, b, c \in \mathrm{~N}$. Then $a+b+c$ is equal to
Let the domain of the function $f(x)=\log _{3} \log _{5} \log _{7}\left(9 x-x^{2}-13\right)$ be the interval $(\mathrm{m}, \mathrm{n})$. Let the hyperbola $\frac{x^{2}}{\mathrm{a}^{2}}-\frac{y^{2}}{\mathrm{~b}^{2}}=1$ have eccentricity $\frac{\mathrm{n}}{3}$ and the length of the latus rectum $\frac{8 \mathrm{~m}}{3}$. Then $\mathrm{b}^{2}-\mathrm{a}^{2}$ is equal to :
The distance between the points (3, 4) and (6, 8) is:
If P is a point on the circle $x^{2}+y^{2}=4, \mathrm{Q}$ is a point on the straight line $5 x+y+2=0$ and $x-y+1=0$ is the perpendicular bisector of PQ, then 13 times the sum of abscissa of all such points P is $\_\_\_\_$.
Let a point $A$ lie between the parallel lines $L_{1}$ and $L_{2}$ such that its distances from $L_{1}$ and $L_{2}$ are 6 and 3 units, respectively. Then the area (in sq. units) of the equilateral triangle $A B C$, where the points $B$ and C lie on the lines $\mathrm{L}_{1}$ and $\mathrm{L}_{2}$, respectively, is :
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