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Q. The tangent to the parabola $y^2=4x$ at the point where it intersects the circle $x^2+y^2=5$ in the first quadrant, passes through the point :

1. $(-\frac{1}{3},\frac{4}{3})$
2. $(-\frac{1}{4},\frac{1}{2})$
3. $(\frac{3}{4},\frac{7}{4})$
4. $(\frac{1}{4},\frac{3}{4})$

Q.

The equation of the tangent at $(x_1,y_1)$ to a curve $y^2=4ax$ at a point $(x_1,y_1)$ is given by $y{y}_1=2a(x+x_1)$

1. True

2. False

Q.

A tangent to the parabola $y^2=4ax$ meets x axis at a point T. This tangent meets the tangent at the vertex at point P. If rectangle TAPQ is completed then the locus of Q is.

1. Circle

2. Straight line

3. parabola

4. Ellipse

Q. If the eccentricity of the standard hyperbola passing through the point $(4,6)$ is $2$, then the equation of the tangent to the hyperbola at $(4,6)$ is :

1. $3x-2y=0$
2. $2x-y-2=0$
3. $2x-3y+10=0$
4. $x-2y+8=0$

Q. If the eccentricity of the standard hyperbola passing through the point $(4,6)$ is $2$, then the equation of the tangent to the hyperbola at $(4,6)$ is :

1. $3x-2y=0$
2. $2x-y-2=0$
3. $2x-3y+10=0$
4. $x-2y+8=0$

Q.

Find the equation of tangent to parabola $y^2=4axat(a{t}^2,2at)$

1. $ty=x+a{t}^2$

2. $y=tx+a{t}^2$

3. $ya{t}^2=x+t$

4. $y+tx=a{t}^2$