Question

Question 18 If p is the length of perpendicular from the origin to the line whose intercepts on the axes are a and b, then show that 1/p^2 = 1/a^2 + 1/b^2.

Class X1 - Maths -Straight Lines Page 228

Answer 1

concept : use intercept form of line : x/a + y/b = 1 and then find perpendicular distance of point from line .


equation of line in intercept form is
x/a + y/b = 1
x/a + y/b - 1 = 0 .

now, use formula
distance of point (x1, y1) from line : ax + by + c =0 is |ax1 + by1 + c|/√(a²+b²)

so, it's distance from origin is
P = | 0 + 0 -1|/√(1/a² + 1/b²)
P = 1/√(1/a² + 1/b²)
1/P = √(1/a² + 1/b²)
take square both sides,
1/P² = 1/a² + 1/b²

hence proved.

Answer 2

This is the answer. Please mark me as brainliest