The parabola y=x2-9 and y=k x2 intersect each other at the points A and B. If the length A B is equal to 10 units then the value of k is equal to

Question

The parabola y=x2-9 and y=k x2 intersect each other at the points A and B. If the length A B is equal to 10 units then the value of k is equal to (A) 75 (B) (9/25) (C) (16/25) (D) (16/9)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/a1fd383861327f5fd0d86b01c45c9308-.png" /> x 2-9= kx 2 x 2( k -1)+0 . x +9=0 x 1+ x 2=0 x 1 x 2=(9/ k -1) now | x 1- x 2|=10=√( x 1+ x 2)2-4 x 1 x 2 100=(36/1- k ) 100-100 k =36 ⇒ k =(64/100)=(16/25)

Q. The parabola $y = x^{2} - 9$ and $y = k x^{2}$ intersect each other at the points $A$ and $B$ . If the length $A B$ is equal to 10 units then the value of $k$ is equal to

75

$\frac{9}{25}$

$\frac{16}{25}$

$\frac{16}{9}$

$x^{2} - 9 = k x^{2}$
$x^{2} (k - 1) + 0. x + 9 = 0$
$x_{1} + x_{2} = 0& x_{1} x_{2} = \frac{9}{k - 1}$
now $∣ x_{1} - x_{2} ∣ = 10 = (x_{1} + x_{2})^{2} - 4 x_{1} x_{2}$
$100 = \frac{36}{1 - k}$
$100 - 100 k = 36 \Rightarrow k = \frac{64}{100} = \frac{16}{25}$

Q. The parabola y=x2−9 and y=kx2 intersect each other at the points A and B. If the length AB is equal to 10 units then the value of k is equal to

75

259​

2516​

916​

x2−9=kx2 x2(k−1)+0.x+9=0 x1​+x2​=0&x1​x2​=k−19​ now ∣x1​−x2​∣=10=(x1​+x2​)2−4x1​x2​​ 100=1−k36​ 100−100k=36⇒k=10064​=2516​

Q. The parabola $y = x^{2} - 9$ and $y = k x^{2}$ intersect each other at the points $A$ and $B$ . If the length $A B$ is equal to 10 units then the value of $k$ is equal to

$\frac{9}{25}$

$\frac{16}{25}$

$\frac{16}{9}$

$x^{2} - 9 = k x^{2}$
$x^{2} (k - 1) + 0. x + 9 = 0$
$x_{1} + x_{2} = 0& x_{1} x_{2} = \frac{9}{k - 1}$
now $∣ x_{1} - x_{2} ∣ = 10 = (x_{1} + x_{2})^{2} - 4 x_{1} x_{2}$
$100 = \frac{36}{1 - k}$
$100 - 100 k = 36 \Rightarrow k = \frac{64}{100} = \frac{16}{25}$