Let RS be the diameter of the circle $x^{2} + y^{2} = 1$ , where S is the point (1, 0). Let P be a variable point (other than R and S) on the circle and tangents to the circle at S and P meet at the point Q. The normal to the circle at P intersects a line drawn through Q parallel to RS at point E. Then, the locus of E passes through the point(s)

Q. A variable circle always touches the line

y - x

and passes through the point

(0, 0)

. The common chords of above circle and

x^{2} + y^{2} + 6 x + 8 y - 7 = 0

will pass through a fixed point whose coordinates are

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A tangent to the ellipse x225+y216=1 at any point P meets the line x=0 at a point Q. Let R be the image of Q in the line y=x. Then the circle, whose extremities of a diameter are Q and R, passes through a fixed point whose coordinates are

The correct option is B (0,0)x225+y216=1P(5cosθ,4sinθ)Tangent x5cosθ+y4sinθ=1Q(θ,4sinθ)R(4sinθ,θ)Cicle with QR as diameter (x−x1)(x−x2)+(y−y1)(y−y2)=0⇒x(x−4sinθ)+y(y−4sinθ)=0passes through (0,0)

A tangent to the ellipse $\frac{x^{2}}{25} + \frac{y^{2}}{16} = 1$ at any point $P$ meets the line $x = 0$ at a point $Q$ . Let $R$ be the image of $Q$ in the line $y = x$ . Then the circle, whose extremities of a diameter are $Q$ and $R$ , passes through a fixed point whose coordinates are