Equation of Tangent in Slope Form

Q. The equations of the tangents to the circle $x^2+y^2$ - 4x - 6y - 12 = 0 and parallel to 4x - 3y = 1 are

1. 4x + 3y + 14 = 0, 4x + 3y + 16 = 0
2. 4x – 3y – 24 = 0, 4x – 3y + 26 = 0
3. x – y – 14 = 0, x – y + 16 = 0
4. 4x – 3y + 34 = 0, 4x – 3y + 16 = 0

Q.

The equations of the tangents to the circle $x^2+y^2=36$ which are inclined at an angle of ${45}^o$ to the x-axis are

1. 

2. 

3. 

4. 

Q.

Find the equation of the circle concentric with the circle $2x^2+2y^2+8x+10y-39=0$and having its area equal to $16\pi$ sq units.

Or

Find the equation of the hyperbola whose conjugate axis is 5 and the distance between foci is 13.

Q.

The equation of tangent with slope m of the circle $x^2+y^2=a^2$ are given by $y=mx\pm m\sqrt{1+a^2}$

1. True

2. False

Q. The slope m of a tangent through the point (7, 1) to the circle $x^2+y^2=25$ satisfies the equation

1. + 7m - 12 = 0
2. + 7m + 9 = 0
3. - 7m - 12 = 0
4. + 12m + 16 = 0

Q.

The equation of the common tangent of the two touching circles, $y^2+x^2-6x-12y+37=0$ and $x^2+y^2-6y+7=0$ is:

1. $x+y-5=0$

2. $x-y+5=0$

3. $x-y-5=0$

4. $x+y+5=0$

Q.

if the equation of tangent to the circle $x^2+y^2-6x+4y-12=0$ which are parallel to the line 4x+3y+5=0 is ax+by+c=0, find the value of $-(\frac{a}{b}+\frac{c}{b})$, where $\left|\frac{c}{a}\right|>6$

___

Q.

If the tangents at P(t1) and Q(t2) in the parabola $y^2=4ax$ meet in T, then find the coordinates of point T.

1. 

2. 

3. 

4. None of these

Q. Let $x^2+y^2-4x-2y-11=0$ be a circle. A pair of tangents from the point (4, 5) with a pair of radii form a quadrilateral of area ___.

Q.

If two circles which pass through the points (0, a) and (0, -a) cut each other orthogonally and touch the straight line $y=mx+c$, then

1. $c^2=a^2(1+m^2)$
2. $c^2=a^2|1+m^2|$
3. $c^2=a^2(2+m^2)$
4. $c^2=2a^2(1+m^2)$

Q. Tangents drawn from the point P(1, 8) to the circle $x^2+y^2-6x-4y-11=0$ touch the circle at points A and B. The equation of the circumcircle of triangle PAB is

1. $x^2+y^2+4x-6y+19=0$
2. $x^2+y^2-4x-10y+19=0$
3. $x^2+y^2-2x+6y-20=0$
4. $x^2+y^2-6x-4y+19=0$