Question

If the length of perpendicular from (-1,2)to the line 3x+ky-4=0 is 3 then k=

Answer 1

Final Answer:

The value of k is $\frac{3{\sqrt{5}}+7}{2}$ or 6.85, for the condition that the length of the perpendicular from $(-1,2)$ to the line $3x+ky-4=0$ is 3.

Given:

The length of the perpendicular from $(-1,2)$ to the line $3x+ky-4=0$ is 3.

To Find:

The value of $k$ in the line $3x+ky-4=0$ .

Explanation:

The perpendicular to any straight line is the definite line which is at right angles to the straight line.

The formula for the length of the perpendicular from $(h,k)$ to the line $x+y+c=0$ is

$=\frac{hx+ky+c}{\sqrt{h^2+k^2}}$

Step 1 of 2

Using the formula, the length of the perpendicular from $(-1,2)$ to the line $3x+ky-4=0$ is

$=\frac{3.(-1)+k.2-4}{\sqrt{(-1)^2+2^2}}\\=\frac{-3+2k-4}{\sqrt{1+4}}\\=\frac{2k-7}{\sqrt{5}}$

Step 2 of 2

Since, the length of the perpendicular from $(-1,2)$ to the line $3x+ky-4=0$ is 3, we can write the following equation.

$\frac{2k-7}{\sqrt{5}}=3\\2k-7=3{\sqrt{5}}\\2k=3{\sqrt{5}}+7\\k=\frac{3{\sqrt{5}}+7}{2}=6.85$

Therefore, the required value of k is $\frac{3{\sqrt{5}}+7}{2}$ or 6.85, when  the length of the perpendicular from $(-1,2)$ to the line $3x+ky-4=0$ is 3.

Know more from the following links.

https://brainly.in/question/375362

https://brainly.in/question/14648814

#SPJ1