Equation of a Chord When Its Mid Point Is Given

Q.

From the origin chords are drawn to the circle $(x-1{)}^2+y^2=1$. The equation of the locus of the middle points of these chords is

1. 

2. 

3. 

4. 

Q. The locus of the point of intersection of the lines bxt-ayt=ab and bx+ay=abt is

1. A parabola

2. An ellipse

3. A hyperbola

4. None of these

Q. The circle passing through three distinct points $(1,t),(t,1)$ and $(t,t)$ for all values of $t$, also passes through the point:

1. $(1,1)$
2. $(-1,-1)$
3. $(1,-1)$
4. $(-1,1)$

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

Q. The equation of chord to the parabola $y^2=4x$ whose sum of ordinates and product of abscissas of the endpoints of the chord is $4$ and $9$ respectively, is :

1. $2x-2y+6=0$
2. $2x-2y-6=0$
3. $3x-2y+3=0$
4. $3x-2y-3=0$

Q. If the tangent and normals at the extremities of a focal chord of a parabola intersect at $(x_1,y_1)$ and $(x_2,y_2)$ respectively, then

1. $x_1=x_2$
2. $x_1=y_2$
3. $y_1=y_2$
4. $y_1=x_2$

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.

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