Equation of a Chord When Its Mid Point Is Given

Q. Slope of tangent to $x^2=4y$ from (-1, -1) can be

1. $\frac{-1\pm \sqrt{5}}{2}$
2. $\frac{-3-\sqrt{5}}{2}$
3. $\frac{1-\sqrt{5}}{2}$
4. $\frac{1+\sqrt{5}}{2}$

Q. Tangents are drawn from the points on the parabola $y^2=-8(x+4)$ to the parabola $y^2=4x.$ Then the locus of mid-point of chord of contact of $y^2=4x$ is

1. $5y^2=8(x+4)$
2. $5y^2=-4(x-4)$
3. $5y^2=8(x-4)$
4. $5y^2=-4(x+4)$

Q. The locus of the midpoints of the focal chords of the parabola $y^2=4ax$ is

1. $y^2=2a(x+a)$
2. $y^2=2a(x-a)$
3. $y^2=2a(2x+a)$
4. $y^2=a(2x-a)$

Q. If the tangent at the point $P(2,4)$ to the parabola $y^2=8x$ meets the parabola $y^2=8x+5$ at $Q$ and $R$, then the mid-point of $QR$ is

1. $(4,2)$
2. $(2,4)$
3. $(7,9)$
4. none of these

Q. The equation(s) of tangents drawn from the point $(1,4)$ to the parabola $y^2=12x$ is/are

1. $x-y+3=0$
2. $x-y+1=0$
3. $x-2y+4=0$
4. $3x-y+1=0$

Q. The equation(s) of tangents drawn from the point $(1,4)$ to the parabola $y^2=12x$ is/are

1. $x-y+3=0$
2. $x-y+1=0$
3. $x-2y+4=0$
4. $3x-y+1=0$

Q. Tangents are drawn from the points on the parabola $y^2=-8(x+4)$ to the parabola $y^2=4x.$ Then the locus of mid-point of chord of contact of $y^2=4x$ is

1. $5y^2=8(x+4)$
2. $5y^2=-4(x-4)$
3. $5y^2=8(x-4)$
4. $5y^2=-4(x+4)$

Q.

Find the locus of mid-point of chord of
parabola $y^2=4x$ which touches the parabola $x^2=4y$.

1. $x^3+2xy+4=0$

2. $y^3+2xy+4=0$

3. $x^3-2xy+4=0$

4. $y^3-2xy+4=0$