`r=a(1 - sinθ) " "&" " r=a(1 + sinθ)`
Find the intersection point `theta`.

x = a(θ - sinθ), y = a(1 + cosθ) Find dy/dx

If the tangent to the ellipse x^(2)+2y^(2)=1 at point P((1)/(sqrt(2)),(1)/(2)) meets the auxiliary circle at point R and Q, then find the points of intersection of tangents to the circle at Q and R.

if 2(2 sin theta -1)x^(2)+8x+4(1+sin theta)geforall x in R then find the general solution of theta

If r gt 0, - pi le theta le pi and r, theta satisfy r sin theta =3 and r=4(1+ sin theta ) , then find the possible solutions of the pair (r , theta )

Tangents drawn to the parabola y^(2)=8x at the points P(t_(1)) and Q(t_(2)) intersect at a point T and normals at P and Q intersect at a point R such that t_(1) and t_(2) are the roots of equation t^(2)+at+2=0;|a|>2sqrt(2) then locus of R is

Find the vector equation of that plane which are passes through the intersection point of r.(2i+2j-3k)=7 and r.(2i+5j+3k)=90 and (2,1,3)

The figure shows a fixed circle C_1 with equation (x-1)^2 +y^2 = 1 and a shrinking circle C_2 with radius r and centre at the origin. P is the point (0,r), Q is the upper point of intersection of the two circles and R is the point of intersection of the line PQ and the x-axis. The coordinates of the point R as C, shrinks ie. as r->0 is