Dr. SK Goyal Solutions for Chapter: Parabola, Exercise 7: Multiple Choice II

A tangent to the parabola $y^2=4ax$ is inclined at $\frac{\pi }{3}$ with the axis of the parabola. The point of contact is

The value of $\lambda$ for which the equation ${\left(10x-5\right)}^2+{\left(10y-7\right)}^2={\lambda }^2{\left(5x+12y+7\right)}^2$ represents the parabola is :

$P$ is a point which moves in the $x-y$ plane, such that the point $P$ is nearer to the centre of a square than any of the sides. The four vertices of the square are $\left(\pm a,\pm a\right)$. The region in which $P$ will move is bounded by parts of parabolas of which one has the equation:

The figure shows the graph of the parabola $y=a{x}^2+bx+c$ then

The equation of a locus is $y^2+2ax+2by+c=0$. Then:

Equation of a tangent to the parabola $y^2=12x$ which make an angle of ${45}^{°}$ with line $y=3x+77$ is

If the tangents drawn from the point $\left(0,2\right)$ to the parabola $y^2=4ax$ are inclined at an angle of $\frac{3\pi }{4}$ then the value of $a$ is:

A chord $PP\text{'}$ of a parabola cuts the axis of the parabola at $O$. The feet of the perpendiculars from $P$ and $P\text{'}$ on the axis are $M$ and $M\text{'}$ respectively. If $V$ is the vertex then $VM,VO,VM\text{'}$ are in: