Question

which of the above statement is correct​

Answer 1

Answer: Both the statements are wrong.

Given:

1. Equation of a line x cosθ + y sinθ = p and a point (α, β).
2. Equation of a line $\frac{x}{a} + \frac{y}{b} =1$ and a point (α, β).

To find: Here we have to find out the length of perpendicular from a point $(x_1, y_1)$ to a line $Ax+By+C=0$ using $d=\frac{|Ax_1+By_1+C|}{\sqrt{A^{2} +B^2}}$

Step-by-step explanation:

For first equation x cosθ + y sinθ = p and a point (α, β)

Here, $A=cos\theta$, $B=sin\theta$ and $C=-p$

Step 1: The length of perpendicular

$d=\frac{|\alpha \cos\theta+\beta \sin\theta-p|}{\sqrt{cos^{2}\theta+sin^2\theta } }$

Step 2: $d={|\alpha \cos\theta+\beta \sin\theta-p|}$

So from the above equation we can say that statement one is wrong.

For second equation $\frac{x}{a} + \frac{y}{b} =1$ and a point (α, β).

Here, $A=\frac{1}{a}$, $B=\frac{1}{b}$ and $C=-1$

Step 1: The length of perpendicular

$d=|\frac{(\frac{\alpha}{a})+(\frac{\beta }{b})-1} {\sqrt{(\frac{1}{a})^2 +(\frac{1}{b})^2}}|$

Step 2: $d=|\frac{\alpha b+\beta a-ab} {\sqrt{({a})^2 +({b})^2}}|$

So from the above equation we can say that statement two is wrong.

To learn more about linear equation questions refer to the link below

https://brainly.in/question/43834340

https://brainly.in/question/34925515

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