Coordinate Geometry PYQ — Page 21

A circle passes through the points $(2,3)$ and $(4$, 5). If its centre lies on the line, $y-4 x+3=0$, then its radius is equal to

The radius of a circle, having minimum area, which touches the curve $y=4-{x}^{2}$ and the lines, $y=|x|$ is:

The locus of the point of intersection of the straight lines, $tx-2y-3t=0$ and $x-2ty+3=0 (t\in R),$ is:

The eccentricity of an ellipse whose centre is at the origin is $\frac{1}{2}$ . If one of its directrices is $x=-4$ , then the equation of the normal to it at $(1,\frac{3}{2})$ is:

The eccentricity of an ellipse having centre at the origin, axes along the co-ordinate axes and passing through the points $(4,-1)$ and $(-2,2)$ is

Let $k$ be an integer such that the triangle with vertices $(k,-3k), (5,k)$ and $(-k, 2)$ has area $28$ sq. units. Then the orthocenter of this triangle is at the point:

If two parallel chords of a circle, having diameter $4$ units, lie on the opposite sides of the center and subtend angles ${\mathrm{cos}}^{-1}⁡(\frac{1}{7})$ and ${\mathrm{sec}}^{-1}⁡(7)$ at the center respectively, then the distance between these chords is:

If a point $P(0,-2)$ and $Q$ is any point on the circle, ${x}^{2}+{y}^{2}-5x-y+5=0$, then the maximum value of ${(PQ)}^{2}$ is

Consider an ellipse, whose center is at the origin and its major axis is along the $x$-axis. If its eccentricity is $\frac{3}{5}$ and the distance between its foci is $6$, then the area (in sq. units) of the quadrilateral inscribed in the ellipse, with the vertices as the vertices of the ellipse, is:

A square, of each side $2$, lies above the $x$-axis and has one vertex at the origin. If one of the sides passing through the origin makes an angle $30^{\circ}$ with the positive direction of the $x$-axis , then the sum of the $x$-coordinates of the vertices of the square is$:$

A line drawn through the point $P(4,7)$ cuts the circle ${x}^{2}+{y}^{2}=9$ at the points $A$ and $B$. Then ${P}_{A}\cdot {P}_{B}$ is equal to.

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 ?

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

The eccentricity of the hyperbola whose length of its conjugate axis is equal to half of the distance between its foci, 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

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

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:

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:

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

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 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 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 ?

The points $(0,\frac{8}{3}),(1,3)$ and $(82,30)$

The number of common tangents to the circles ${x}^{2} + {y}^{2} - 4 x - 6 y - 1 2 = 0$ and ${x}^{2}+{y}^{2}+6x+18y+26=0$, is