Curve x2+2y2=2 intersect the line x+y=1 at points P and Q. First we have to find any common relation between these two curves. Use substitution for the same as follows, x2+2y2‌‌=2 . . . (i) x+y‌‌=1,‌ then ‌(x+y)2=12 ⇒‌‌x2+y2+2xy=1. . . (ii) We can write Eq. (i) as, x2+2y2−2(1)2=0 ⇒‌‌x2+2y2−2(x+y)2=0 ⇒x2+2y2−2x2−2y2−4xy=0 ⇒‌‌−x2−4xy=0⇒−x(x+4y)=0 Gives, x=0 and x+4y=0 or y=‌
−1
4
x Draw the line y=‌
−1
4
x on graph and take arbitrary point (any one) as follows, From given graph,
tan‌θ=‌
1
4
⇒θ=tan−1(‌
1
4
) We have two lines, y=−‌
1
4
x and x=0 (i.e. Y - axis). Thus, any line joining these two curves makes an angle ‌
