The straight line 2x - 3y = 1 divides the cir | vedclass

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

Question

(B) Let the circle be $C: x^2 + y^2 - 6 = 0$ and the line be $L: 2x - 3y - 1 = 0$.First,check which points lie inside the circle $x^2 + y^2 \leq 6$:$1

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(B) Let the circle be $C: x^2 + y^2 - 6 = 0$ and the line be $L: 2x - 3y - 1 = 0$.First,check which points lie inside the circle $x^2 + y^2 \leq 6$:$1$. For $(2, 3/4)$: $2^2 + (3/4)^2 = 4 + 9/16 = 73/16 = 4.5625 $2$. For $(5/2, 3/4)$: $(5/2)^2 + (3/4)^2 = 25/4 + 9/16 = 109/16 = 6.8125 > 6$ (Outside).$3$. For $(1/4, -1/4)$: $(1/4)^2 + (-1/4)^2 = 1/16 + 1/16 = 2/16 = 0.125 $4$. For $(1/8, 1/4)$: $(1/8)^2 + (1/4)^2 = 1/64 + 1/16 = 5/64 = 0.078 Now,check which side of the line $L(x, y) = 2x - 3y - 1$ these points lie on. The center of the circle $(0, 0)$ gives $L(0, 0) = -1 $1$. For $(2, 3/4)$: $L = 2(2) - 3(3/4) - 1 = 4 - 9/4 - 1 = 3 - 2.25 = 0.75 > 0$.$2$. For $(1/4, -1/4)$: $L = 2(1/4) - 3(-1/4) - 1 = 1/2 + 3/4 - 1 = 1.25 - 1 = 0.25 > 0$.$3$. For $(1/8, 1/4)$: $L = 2(1/8) - 3(1/4) - 1 = 1/4 - 3/4 - 1 = -1.5 Since $L(0, 0) = -1$,the region containing the origin is $L  0$. The points $(2, 3/4)$ and $(1/4, -1/4)$ satisfy $L > 0$ and are inside the circle. Thus,there are $2$ such points.

Similar Questions

If $(6, -k)$ and $(-3, 2)$ are conjugate points with respect to the circle $x^2 + y^2 + 6x + 4y + 12 = 0$,then $k$ equals:

If a circle with centre at $(-1, 1)$ touches the line $x + 2y + 4 = 0$,then the coordinates of the point of contact are:

Two circles each of radius $5 \text{ units}$ touch each other at the point $(1, 2)$. If the equation of their common tangent is $4x + 3y = 10$,and $C_{1}(\alpha, \beta)$ and $C_{2}(\gamma, \delta)$,$C_{1} \neq C_{2}$ are their centres,then $|(\alpha + \beta)(\gamma + \delta)|$ is equal to .... .

The set of values of $k$ for which the circle $C : 4x^{2} + 4y^{2} - 12x + 8y + k = 0$ lies inside the fourth quadrant and the point $(1, -1/3)$ lies on or inside the circle $C$ is

The length of the chord intercepted by the circle $x^2 + y^2 = 1$ on the line $x + y = 1$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module