Question

ncert class 11 math chapter straight line s exercise 10.3 question no 16

Answer 1

draw a diagram ( draw two straight line p and q passes through origin for p x cos TheetA - y sin TheetA = k cos 2 TheetA , for q x sec TheetA + y cosec TheetA= k), first we find p length by using formula for distance of a point from a line, p = mode 0 into cos TheetA - 0 into sin TheetA - k cos 2 TheetA/ under root cos square TheetA + sin square TheetA, mode - k cos 2 TheetA / root 1, p= mode k cos 2 TheetA, x sec TheetA + y cosec TheetA= k, x/cos TheetA + y/sin TheetA=k, x sin TheetA +y cos TheetA/ sin TheetA cos TheetA=k, x sin TheetA +ycos TheetA= k2sin TheetA cos TheetA/2( multiply by 2 and divide by 2), x sin TheetA +ycos TheetA= ksin2theeta/2, xsin TheetA + ycos TheetA -ksin2theeta/2, q= mode 0 into sin TheetA + y cos TheetA - ksin 2 TheetA/2/ root 1, q= ksin2 TheetA/2, L.H.S = p square + 4 q square, we put the value of p and q, (kcos2 TheetA) square +4(ksin 2 TheetA/2) square, k square cos square 2 TheetA + 4 into k square sin square 2 TheetA/4, k square ( cos square 2 TheetA+ sin square 2 TheetA ), k square into 1, k square hence proved (I am requesting you to please Mark it as a brainiest)