Expression 'S1'

Q. If the line passing through P = (8, 3) meets the circle $S\equiv x^2+y^2-8x-10y+26=0$ at A, B then PA · PB =

1. 5
2. 14
3. 4
4. 24

Q. Length of the tangent drawn from any point on the circle $x^2+y^2+2gx+2fy+c_1=0$ to the circle is $x^2+y^2+2gx+2fy+c=0$

1. $\sqrt{c_1-c}$
2. $\sqrt{c-c_1}$
3. $\sqrt{c_1+c}$
4. None of these

Q.

The point $(x_1,y_1)$ lies inside the circle $x^2+y^2+2gx+2fy+c=0$, if $x_1^2+y_1^2+2g{x}_1+2f{g}_1+c$ is less than zero

1. True

2. False

Q.

Which of the following point lie inside the circle $x^2+y^2-2x+3y-11=0$

1. (1, 1)

2. (-1, 2)

3. (3, 2)

4. (2, 3)

Q.

Let us get familiarized with some terms.

1) S: It is the equation of circle.

$S_1$: We get $S_1$ by substituting a point $x_1,y_1$ in the equation of the circle

$S_1=x_1^2+y_1^2+2g{x}_1+2f{y}_1+c$

2) T: We get T by replacing $x_2$ with $x{x}_1,y_2$ with $y{y}_1,x$ with $\frac{x+x_1}{2},y$ with $\frac{y+y_1}{2}$ and $xy$ wih $\frac{x{y}_1+y{x}_1}{2}.C$

remains the same

$T\equiv x{x}_1+y{y}_1+g(x+x_1)+f(y+y_1)+c$

These are really helpfull in finding the equation of tangent; chord of contact, pair of tangents from

appoint and determining if a point lies inside a circle.

If $S_1<0$, the point lies inside the circle

If $S_1=0$ the point lies on the circle and if $S_1>0$ the point lies outside the circle.

If you are comfortable and read this, click true to more to the question.

1. True

2. False