Equation of Tangent in Point Form

Q. The line 4x + 4y – 11 = 0 intersects the circle $x^2+y^2-6x-4y+4=0$ at A and B. The point of intersection of the tangents at A, B is

1. (–1, – 2)
2. (1, 2)
3. (–1, 2)
4. (1, –2)

Q.

The radius of the circle passing through the point $P(6,2)$, two of whose diameters are $x+y=6$ and $x+2y=4$ is

1. $10$
2. $2\sqrt{5}$
3. $6$
4. $4$

1. $10$

2. $2\sqrt{5}$

3. $6$

4. $4$

Q.

If the point of contact of the circle $x^2+y^2-30x+6y+109=0$ with the tangent 11x - 2y - 46 = 0 is (a, b), find a + b

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Q. If the line x + y = 5 is a tangent to the circle $x^2+y^2-2x-4y+3=0$, then the coordinates of the point of contact are .

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

Q. If a tangent to the circle $x^2+y^2=1$ intersects the coordinate axes at distinct points $P$ and $Q$, then the locus of the mid-point of $PQ$ is:

1. $x^2+y^2-2xy=0$
2. $x^2+y^2-2x^2{y}^2=0$
3. $x^2+y^2-4x^2{y}^2=0$
4. $x^2+y^2-16x^2{y}^2=0$

Q. The equation of the tangent drawn to the circle $x^2+y^2=4$ at the point whose polar coordinates are given by $(2,\frac{\pi }{3})$ is

1. $x+\sqrt{3}y=2$
2. $\sqrt{3}x+y=2$
3. $x+\sqrt{3}y=4$
4. $\sqrt{3}x+y=4$

Q. A chord of the circle $x^2+y^2-4x-6y=0$ passing through the origin subtends an angle $ta{n}^{-1}\left(\frac{7}{4}\right)$ at the point where the circle meets positive y-axis. Equation of the chord is

1. 2x + 3y = 0
2. x + 2y = 0
3. x – 2y = 0
4. 2x – 3y = 0

Q. The equation of the tangents to the circle $x^2+y^2=a^2$, which makes a triangle of area $a^2$ sq. units with coordinate axes, is/are

1. $x+y=a\sqrt{2}$
2. $x-y=a\sqrt{2}$
3. $2x+3y=2a\sqrt{3}$
4. $2x-3y=2a\sqrt{3}$

Q. Two tangents are drawn on the circle $x^2+y^2-6x-2y-15=0$ at point $B(3,6)$ and $D(0,-3)$ which meets at point $C$. If $A$ be the center of circle, then area of quadrilateral $ABCD$ is

Q. The point of contact of the tangent to the circle $x^2+y^2=5$ at the point (1, -2) which touches the circle $x^2+y^2-8x+6y+20=0$, is

1. (2, -1)
2. (3, -1)
3. (4, -1)
4. (5, -1)

Q.

If the point of contact of the circle $x^2+y^2-30x+6y+109=0$ with the tangent 11x - 2y - 46 = 0 is (a, b), find a + b

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Q. The circle $C_1:x^2+y^2=8$ cuts orthogonally the circle $C_2$ whose centre lies on the line $x-y-4=0$ then, the circle $C_2$ passes through a fixed point, which lies on

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

Q. Consider the relation $4l^2-5m^2+6l+1=0$, where $l,m\in R.$ If the line $lx+my+1=0$ touches a fixed circle, then the centre of that circle is:

1. $(0,5)$
2. $(3,0)$
3. $(2,1)$
4. $(3,-3)$

Q. From the point $(1,-2,3)$, lines are drawn to meet the sphere $x^2+y^2+z^2=4$ and they are divided internally in the ratio $2:3$. The locus of the point of division is

1. $5x^2+5y^2+5z^2-6x+12y+2z=0$
2. $5x^2+5y^2+5z^2-2xy-3yz-zx-6x+12y+5z=0$
3. $5(x^2+y^2+z^2)=22$
4. None of these