Pair of Tangents, Chord of Contact and Chord with Midpoint of a Parabola

The locus of the mid-points of the chords of the parabola $x^2=4py$ having slope $m$ is $a$

If $y=mx$ bisect two chords of $y^2=4x$ from $(4,4),$ then $m$ can't be

The locus of the mid-points of the chords of the parabola $y^2=4ax,$ which passes through the origin is

From the point $(4,6),$ a pair of tangent lines are drawn to the parabola $y^2=8x.$ Find the area of the triangle formed by these pair of tangent lines and the chord of contact of the point $(4,6)$.

If the chord of contact of tangents from a point $P$ to the parabola $y^2=4ax$ touches the parabola $x^2=4by$, then find the locus of $P$.

Consider the chords of the parabola $y^2=4x$ which touches the hyperbola $x^2-y^2=1$. A conic section is formed on tracing the locus of the point of intersection of the tangents drawn to the parabola at the extremities of such chords. If $\lambda$ represents the length of the conic section's latus rectum, then $\lambda$ is

Cotyledons are also called-

If $P$ is a point on the parabola $y^2=8x$ and $A$ is the point $(1,0)$, then the locus of the midpoint of the line segment $AP$ is

The length of the common chord of the parabolas $y^2=x$ and $x^2=y$ and is

The locus of the middle points of the chords of the parabola $y^2=4ax,$ which passes through the origin is

Equation of chord of the parabola $y^2=16x$ whose mid point is (1, 1), is

Locus of midpoint of any focal chord of $y^2=4ax$ is

Locus of mid point of any focal chord of $y^2=4ax$ is

Locus of mid point of any focal chord of $y^2=4ax$ is

Locus of midpoint of any focal chord of $y^2=4ax$ is

Locus of mid point of any focal chord of $y^2=4ax$ is

The angle between the tangent drawn from the point $\left(1,4\right)$ to the parabola $y^2=4x$ is

Locus of midpoint of any focal chord of $y^2=4ax$ is

Two tangents are drawn from a point $\left(-2,-1\right)$ to the curve $y^2=4x$. If $\alpha$ is the angle between them, then $\left|\tan \alpha \right|$ is equal to

Two tangents are drawn from a point $(-2, -1)$ to the curve, $y^2 = 4x.$ If $\alpha$ is the angle between them, then $|\tan \alpha |$ is equal to :