A point inside the circle x^2 + y^2 + 3x - 3y | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Let the equation of the circle be $S(x, y) = x^2 + y^2 + 3x - 3y + 2 = 0$.$A$ point $(x_1, y_1)$ lies inside the circle if $S(x_1, y_1) < 0$.Check

Vedclass · Accepted Answer

$(-2, 1)$

Vedclass · Answer

(B) Let the equation of the circle be $S(x, y) = x^2 + y^2 + 3x - 3y + 2 = 0$.$A$ point $(x_1, y_1)$ lies inside the circle if $S(x_1, y_1) Checking option $(A) (-1, 3)$: $S(-1, 3) = (-1)^2 + (3)^2 + 3(-1) - 3(3) + 2 = 1 + 9 - 3 - 9 + 2 = 0$. The point lies on the circle.Checking option $(B) (-2, 1)$: $S(-2, 1) = (-2)^2 + (1)^2 + 3(-2) - 3(1) + 2 = 4 + 1 - 6 - 3 + 2 = -2$. Since $-2 Checking option $(C) (2, 1)$: $S(2, 1) = (2)^2 + (1)^2 + 3(2) - 3(1) + 2 = 4 + 1 + 6 - 3 + 2 = 10$. Since $10 > 0$,the point lies outside the circle.Checking option $(D) (-3, 2)$: $S(-3, 2) = (-3)^2 + (2)^2 + 3(-3) - 3(2) + 2 = 9 + 4 - 9 - 6 + 2 = 0$. The point lies on the circle.Thus,the correct option is $(B)$.

$A$ point inside the circle $x^2 + y^2 + 3x - 3y + 2 = 0$ is

Similar Questions

The points of intersection of the line $4x - 3y - 10 = 0$ and the circle $x^2 + y^2 - 2x + 4y - 20 = 0$ are

If a circle $C$ passing through the point $(4, 0)$ touches the circle $x^2+y^2+4x-6y=12$ externally at the point $(1, -1)$,then the radius of $C$ is

If $(3,-2)$ is the centre of the circle $S \equiv x^2+y^2+2gx+2fy-23=0$ and $A$ is a point on the circle $S=0$ such that its distance from a point $P(-1,-5)$ is least,then $A=$

If $\theta$ is the angle between the tangents from $(-1, 0)$ to the circle $x^2+y^2-5x+4y-2=0$,then $\theta$ is equal to

When do the circles represented by the equations $x^{2} + y^{2} + c^{2} = 2ax$ and $x^{2} + y^{2} + c^{2} = 2by$ touch each other externally?

Vedclass Test Series

Exam Paper Generator

Online Exam Module