If the length of the chord of the circle, x 2+ y 2= r 2( r 0) along the line, y -2 x =3 is r, then r2 is equal to :

Question

If the length of the chord of the circle, x 2+ y 2= r 2( r >0) along the line, y -2 x =3 is r, then r2 is equal to : (A) (9/5) (B) (12/5) (C) 12 (D) (24/5)

Tardigrade Admin · Accepted Answer

Let chord AB = r ∵ Δ AOM is right angled triangle ∴ OM =( r √3/2)= perpendicular distance of line <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/7d0e9b9ea6640c0f1d5eb4ae7d84805d-.png" /> AB from (0,0) ( r √3/2)=|(3/√5)| r2=(12/5)

Q. If the length of the chord of the circle, $x^{2} + y^{2} = r^{2} (r > 0)$ along the line, $y - 2 x = 3$ is $r$ , then $r^{2}$ is equal to :

$\frac{9}{5}$

$\frac{12}{5}$

12

$\frac{24}{5}$

Let chord
$A B = r$
$∵ Δ A OM$ is right angled triangle
$∴ OM = \frac{r 3}{2} =$ perpendicular distance of line

AB from (0,0)
$\frac{r 3}{2} = ∣ ∣ \frac{3}{5} ∣ ∣$
$r^{2} = \frac{12}{5}$

Q. If the length of the chord of the circle, x2+y2=r2(r>0) along the line, y−2x=3 is r, then r2 is equal to :

59​

512​

12

524​

Let chord AB=r ∵ΔAOM is right angled triangle ∴OM=2r3​​= perpendicular distance of line AB from (0,0) 2r3​​=∣∣​5​3​∣∣​ r2=512​

Q. If the length of the chord of the circle, $x^{2} + y^{2} = r^{2} (r > 0)$ along the line, $y - 2 x = 3$ is $r$ , then $r^{2}$ is equal to :

$\frac{9}{5}$

$\frac{12}{5}$

$\frac{24}{5}$

Let chord
$A B = r$
$∵ Δ A OM$ is right angled triangle
$∴ OM = \frac{r 3}{2} =$ perpendicular distance of line

AB from (0,0)
$\frac{r 3}{2} = ∣ ∣ \frac{3}{5} ∣ ∣$
$r^{2} = \frac{12}{5}$