Point Form of Tangent: Hyperbola

Q.

The equations of the tangents to the circle $x^2+y^2=50$ at the points where the line $x+7=0$ meets it, are

1. 

2. 

3. 

4. 

Q. The area of the triangle formed with the coordinate axes and the tangent at the point $(x_1,y_1)$ on the circle $x^2+y^2=a^2$ is

1. 
2. 
3. 
4. 

Q.

If the line $2x+\sqrt{6}y=2$ is tangent to the hyperbola $x^2-2y^2=4$ then the point of contact is.

1. 

2. 

3. 

4. 

Q.

If $2x-y+1=0$ is a tangent to the hyperbola$\frac{x^2}{a^2}-\frac{y^2}{16}=1$, then which of the following CANNOT be sides of a right triangle?

1. $a,4,1$

2. $2a,4,1$

3. $a,4,2$

4. $2a,8,1$

Q. The point on the hyperbola $x^2-9y^2=9$, where the line 5x + 12y = 9 touches it, is .

1. $(5,-\frac{4}{3})$
2. $(-5,\frac{4}{3})$
3. $(-\frac{5}{3},4)$
4. $(\frac{5}{3},-4)$

Q. Tangents are drawn to the hyperbola $\frac{x^2}{9}-\frac{y^2}{4}=1$
parallel to the straight line $2x-y=1$ The points of contacts of the tangents on the hyperbola are

1. $(\frac{9}{2\sqrt{2}},\frac{1}{\sqrt{2}})$
2. $(-\frac{9}{2\sqrt{2}},-\frac{1}{\sqrt{2}})$
3. $(3\sqrt{3},-2\sqrt{2})$
4. $(-3\sqrt{3},2\sqrt{2})$

Q. In a hyperbola portion of tangent intercepted between asymptotes is bisected at the point of contact. Consider a hyperbola whose centre is at origin. A line $x+y=2$ touches this hyperbola at $P(1,1)$ and intersects the asymtotes at $A$ and $B$ such that $AB=6\sqrt{2}$ units.

Equation of the tangent to the hyperbola at $(-1,\frac{7}{2})$ is

1. $5x+2y=2$
2. $3x+2y=4$
3. $3x+4y=11$
4. none of these

Q. If a hyperbola passes through the point P $(\sqrt{2},\sqrt{3})$ and has foci $(\pm 2,0),$ then the tangent to this hyperbola at P also passes through the point

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

Q. The equation of the tangent to the conic $x^2-y^2-8x+2y+11=0$ at $(2,1)$ is:

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

Q.

If the line $2x+\sqrt{6}y=2$ is tangent to the hyperbola $x^2-2y^2=4$ then the point of contact is.

1. $(\sqrt{6},1)$

2. $(2,\sqrt{6})$

3. $(1,\sqrt{6})$

4. $(4,-\sqrt{6})$

Q. A straight line passing through the point A(-1, 2) has inclination of 60°and intersects the line x+y=5 at P. FindAP

Q. Locus of the middle point of the intercept on the line y=x+c made by the lines 2x+3y=5 and 2x+3y=8, c being a parameter, is (1) 2x+3y+13=0 (2) 4x+6y+13=0 (3) 4x+6y-13=0 (4) 2x+3y-13=0