Mathematics Coordinate Geometry questions from JEE Main 2016.
If a variable line drawn through the intersection of the lines $\frac{x}{3}+\frac{y}{4}=1$ and $\frac{x}{4}+\frac{y}{3}=1$ , meets the coordinate axes at $A$ and $B$, $(A \neq B),$then the locus of the midpoint of $\mathrm{AB}$ is:
The eccentricity of the hyperbola whose length of its conjugate axis is equal to half of the distance between its foci, is
Equation of the tangent to the circle, at the point $(1,-1)$, whose center, is the point of intersection of the straight lines $x-y=1$ and $2x+y=3$ is:
Two sides of a rhombus are along the lines, $x-y+1=0$ and $7x-y-5=0$ . If its diagonals intersect at $(-1, -2)$ , then which one of the following is a vertex of this rhombus ?
If one of the diameters of the circle, given by the equation, ${x}^{2}+{y}^{2}-4x+6y-12=0,$ is a chord of a circle $S$, whose centre is at $(-3,2)$, then the radius of $S$ is
The point $(2,1)$ is translated parallel to the line $L:x-y=4$ by $2\sqrt{3}$ units. If the new point $Q$ lies in the third quadrant, then the equation of the line passing through $Q$ and perpendicular to $L$ is
Let $a$ and $b$ respectively be the semi-transverse and semi-conjugate axes of a standard hyperbola whose eccentricity satisfies the equation $9{e}^{2}-18e+5=0$. If $S(5, 0)$ is a focus and $5x=9$ is the corresponding directrix of this hyperbola, then ${a}^{2}-{b}^{2}$ is equal to
A hyperbola whose transverse axis is along the major axis of the conic $\frac{{x}^{2}}{3}+\frac{{y}^{2}}{4}=4$ and has vertices at the foci of the conic. If the eccentricity of the hyperbola is $\frac{3}{2}$, then which of the following points does not lie on the hyperbola $?$
A ray of light is incident along a line which meets another line $7x-y+1=0$ at the point $(0,1)$. The ray is then reflected from this point along the line $y+2x=1$. Then the equation of the line of incidence of the ray of light is :
A circle passes through $(-2,4)$ and touches the $y-$axis at $(0,2)$. Which one of the following equations can represent a diameter of this circle ?
A straight line through origin $O$ meets the lines $3y=10-4x$and $8x+6y+5=0$ at points $A$ and $B$ respectively. Then, $O$ divides the segment $AB$ in the ratio