Coordinate Geometry PYQ — Page 26

If the lines $2 x+3 y+1=0$ and $3 x-y-4=0$ lie along diameters of a circle of circumference $10 \pi$, then the equation of the circle is

Let $A(2,-3)$ and $B(-2,1)$ be vertices of a triangle $A B C$. If the centroid of this triangle moves on the line $2 x+3 y=1$, then the locus of the vertex $C$ is the line

A variable circle passes through the fixed point $A(p, q)$ and touches $x$-axis. The locus of the other end of the diameter through $\mathrm{A}$ is

If a circle passes through the point $(a, b)$ and cuts the circle $x^2+y^2=4$ orthogonally, then the locus of its centre is

Locus of a centriod of the triangle whose vertices are $(a \cos t, a \sin t),(b \sin t,-b \cos t)$ and $(1,0)$, where $t$ is a parameter, is

A square of side a lies above the $x$-axis and has one vertex at the origin. The side passing through the origin makes an angle $\alpha\left(0 < \alpha < \frac{\pi}{4}\right)$ with the positive direction of $\mathrm{x}$-axis. The equation of its diagonal not passing through the origin is

If the two circles $(x-1)^2+(y-3)^2=r^2$ and $x^2+y^2-8 x+2 y+8=0$ intersect in two distinct point, then

The foci of the ellipse $\frac{x^2}{16}+\frac{y^2}{b^2}=1$ and the hyperbola $\frac{x^2}{144}-\frac{y^2}{81}=\frac{1}{25}$ coincide. Then the value of $b^2$ is

The lines $2 \mathrm{x}-3 \mathrm{y}=5$ and $3 \mathrm{x}-4 \mathrm{y}=7$ are diameters of a circle having area as 154 sq. units. Then the equation of the circle is

The vectors $\overrightarrow{\mathrm{AB}}=3 \hat{\mathrm{i}}+4 \hat{\mathrm{k}} \& \overrightarrow{\mathrm{AC}}=5 \hat{\mathrm{i}}-2 \hat{\mathrm{j}}+4 \hat{\mathrm{k}}$ are the sides of a triangle $\mathrm{ABC}$. The length of the median through $\mathrm{A}$ is

If the equation of the locus of a point equidistant from the point $\left(a_1, b_1\right)$ and $\left(a_2, b_2\right)$ is $\left(a_1-b_2\right) x+\left(a_1-b_2\right) y+c=0$, then the value of 'c' is

A triangle with vertices (4, 0), (-1, -1), (3, 5) is

Locus of mid point of the portion between the axes of $x \cos \alpha+y \sin \alpha=p$ where $p$ is constant is

The sides of a triangle are 3x + 4y, 4x+37 and 5x + 57 where x, y > 0 then the triangle is

If the chord $y=m x+1$ of the circle $x^2+y^2=1$ subtends an angle of measure $45^0$ at the major segment of the circle then value of $m$ is