The length of the chord of the circle x2 + y2 + 3x + 2y - 8 = 0 intercepted by the y-axis is

Question

The length of the chord of the circle x2 + y2 + 3x + 2y - 8 = 0 intercepted by the y-axis is (A) 3 (B) 8 (C) 9 (D) 6

Tardigrade Admin · Accepted Answer

Given equation of circle is x2+y2+3 x+2 y-8=0 On comparing with x2+y2+2 g x+2 f y+c=0, we get g=(3/2), f=1 and c=-8 Now, intercept made by y -axis =2 √f2-c =2 √(1)2-(-8) =2 √1+8=2 √9 =2 × 3=6

Q. The length of the chord of the circle $x^{2} + y^{2} + 3 x + 2 y - 8 = 0$ intercepted by the y-axis is

3

8

9

6

Given equation of circle is
$x^{2} + y^{2} + 3 x + 2 y - 8 = 0$
On comparing with
$x^{2} + y^{2} + 2 g x + 2 f y + c = 0,$ we get
$g = \frac{3}{2}, f = 1$ and $c = - 8$
Now, intercept made by $y$ -axis
$= 2 f^{2} - c$
$= 2 (1)^{2} - (- 8)$
$= 2 1 + 8 = 29$
$= 2 \times 3 = 6$

Q. The length of the chord of the circle x2+y2+3x+2y−8=0 intercepted by the y-axis is

3

8

9

6

Given equation of circle is x2+y2+3x+2y−8=0 On comparing with x2+y2+2gx+2fy+c=0, we get g=23​,f=1 and c=−8 Now, intercept made by y -axis =2f2−c​ =2(1)2−(−8)​ =21+8​=29​ =2×3=6

Q. The length of the chord of the circle $x^{2} + y^{2} + 3 x + 2 y - 8 = 0$ intercepted by the y-axis is

Given equation of circle is
$x^{2} + y^{2} + 3 x + 2 y - 8 = 0$
On comparing with
$x^{2} + y^{2} + 2 g x + 2 f y + c = 0,$ we get
$g = \frac{3}{2}, f = 1$ and $c = - 8$
Now, intercept made by $y$ -axis
$= 2 f^{2} - c$
$= 2 (1)^{2} - (- 8)$
$= 2 1 + 8 = 29$
$= 2 \times 3 = 6$