In the $x y$ -plane, the line determined by the points $(2, k)$ and $(k, 32)$ passes through the origin. Which of the following could be the value of $k$ ?

0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

4

No worries! We‘ve got your back. Try BYJU‘S free classes today!

8

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

16

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $8$
Line passes through two points $(2, k)$ and $(k, 32)$ is
$y - k = \frac{32 - k}{k - 2} (x - 2)$ ....using $[y - y 1 = \frac{y 2 - y 1}{x 2 - x 1} (x - x 1)]$
Since, line passes through $(0, 0)$
$∴ 0 - k = \frac{32 - k}{k - 2} (0 - 2)$
$\Rightarrow 2 k - k^{2} = - 64 + 2 k$
$\Rightarrow k^{2} = 64$
$\Rightarrow k = 8, - 8$
Hence, option C is correct.

Suggest Corrections

Similar questions

Q. The line

{(k + 1)}^{2} x + k y - {2 k}^{2} - 25 = 0

passes through a point regardless of the value k. Which of the following is the line slope

2

passing through the point?

For different values of k, the circle $x^{2} + y^{2}$ + (8 + k)x + (8 + k)y + (16 + 12k) = 0, always passes through two fixed point P and Q. For $k = k_{1}$ , the tangents at P and Q intersect at the origin. Which of the following is/are correct?

Q. A straight line passes through the points

A (2, - 4)

and

B (5, - 2)

.
Find the value of

k

, if

A B

passes through the point

P (k + 3, k - 4)

Q. If the curve

2 x^{2} + x y - y^{2} - 3 x + 4 y + k = 0

passes through the origin, then the value of

k

is _____

The line, represented by the equation 3x - 8y = 2, passes through the point (k,5), the value of k is:

Join BYJU'S Learning Program

In the xy-plane, the line determined by the points (2,k) and (k,32) passes through the origin. Which of the following could be the value of k?

The correct option is B 8Line passes through two points (2,k) and (k,32) isy−k=32−kk−2(x−2) ....using [y−y1=y2−y1x2−x1(x−x1)]Since, line passes through (0,0)∴0−k=32−kk−2(0−2)⇒2k−k2=−64+2k⇒k2=64⇒k=8,−8Hence, option C is correct.

In the $x y$ -plane, the line determined by the points $(2, k)$ and $(k, 32)$ passes through the origin. Which of the following could be the value of $k$ ?