Coordinate Geometry Questions

A straight line through the point $A(3,4)$ is such that its intercept between the axes is bisected at $A$. Its equation is:

The two lines $x=ay+b,z=cy+d$; and $x=a^{\prime }y+b^{\prime },z=c^{\prime }y+d^{\prime }$ are perpendicular to each other if:

The locus of the vertices of the family of parabolas $y=\frac{a^3{x}^2}{3}+\frac{a^{2}x}{2}-2a$ is:

In an ellipse, the distance between its foci is $6$ and the minor axis is $8$. Then its eccentricity is:

Angle between the tangents to the curve $y=x^2-5x+6$ at the points $(2,0)$ and $(3,0)$ is:

If the lines $3x-4y-7=0$ and $2x-3y-5=0$ are two diameters of a circle of area $49\pi$ square units, the equation of the circle is:

Let $C$ be the circle with centre $(0,0)$ and radius $3$ units. The equation of the locus of the mid points of the chords of the circle $C$ that subtend an angle of $2\pi /3$ at its centre is:

The image of the point $(-1,3,4)$ in the plane $x-2y=0$ is: