Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Advanced2006MathematicsParabolaActual

Paragraph: Read the following passage and answer the questions. Let A B C D be a square of side length 2 units. C₂ is the circle through vertices A, B, C, D and C₁ is the circle touching all the sides of square A B C D . L is the line through A . Question: A circle touches the line L and the circle C₁ externally such that both the circles are on the same side of the line, then the locus of centre of the circle is

Options

  1. Aellipse
  2. Bhyperbola
  3. Cparabola
  4. Dparts of straight line

Correct answer

C. parabola

Step-by-step solution

Let C be the centre of the required circle. Now, draw a line parallel to L at a distance of r₁ (radius of C₁ ) from it. Now, C P₁=A C C lies on a parabola.

Practice Parabola on Quantrex Academy →

More from Parabola

Let T be the tangent to the parabola y^2 = 16x at the point (64, 32) . Let L be the tangent to the same parabola at another point (x₁, y₁) on the parabola. If L and T are perpendic 2026Let O be the vertex of the parabola y^2=4x and its chords OP and OQ are perpendicular to each other. If the locus of the mid-point of the line segment PQ is a conic C, then the len 2026Let chord PQ of length 3 13 of the parabola y^2 = 12x be such that the ordinates of points P and Q are in the ratio 1:2 . If the chord PQ subtends an angle at the focus of the para 2026Let the point P be the vertex of the parabola y = x^2 - 6x + 12 . If a line passing through the point P intersects the circle x^2 + y^2 - 2x - 4y + 3 = 0 at the points R and S , th 2026Let the directrix of the parabola P: y^2 = 8x , cut x -axis at the point A . Let B( , ) , > 1 , be a point on P such that the slope of AB is 3/5 . If BC is a focal chord of P , the 2026Let A,B and C be the vertices of a variable right angled triangle inscribed in the parabola y^2=16x . Let the vertex B containing the right angle be (4,8) and the locus of the cent 2026Consider the parabola P : y^2 = 4kx and the ellipse E : x^2 a^2 + y^2 b^2 = 1 . Let the line segment joining the points of intersection of P and E , be their latus rectums. If the 2026Let the parabola y = x^2 + px + q passing through the point (1, -1) be such that the distance between its vertex and the x -axis is minimum. Then the value of p^2 + q^2 is: 2026 Full Parabola list All JEE Advanced PYQs