Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
Highly selective Backlog Qs for JEE MainMathematicsCircle

Let x 0 , y 0 be fixed real numbers such that x 0 2 + y 0 2 > 1 . If x , y are arbitrary real numbers such that x 2 + y 2 ≤ 1 , then the minimum value of x - x 0 2 + y - y 0 2 is

Options

  1. Ax 0 2 + y 0 2 - 1 2
  2. Bx 0 2 + y 0 2 - 1
  3. Cx 0 + y 0 - 1 2
  4. Dx 0 + y 0 2 - 1

Correct answer

A. x 0 2 + y 0 2 - 1 2

Step-by-step solution

Let P x 0 , y 0 Given x 2 + y 2 ≤ 1 1 Let any arbitrary point 8 ( x , y ) . P Q 2 = x - x 0 2 + y - y 0 2 P Q 2 = ( O P - O Q ) 2 P Q 2 = ( O P - O Q ) 2 P Q 2 = x 0 2 + x 0 2 - 1 2 [ ∵ 0 Q = 1 ] ∴ Mininimum value of P Q 2 is x 0 2 + y 0 2 - 1 2

Practice Circle on Quantrex Academy →

More from Circle

Match each entry in List-I to the correct entry in List-II and choose the correct option. List-I List-II (P) The circle with centre (1, 2) and touching the straight line 3x + 4y = 2026Consider the circle C: x^2+y^2-6x-8y-11=0 . Let a variable chord AB of the circle C subtend a right angle at the origin. If the locus of the foot of the perpendicular drawn from th 2026Let C be a circle having centre in the first quadrant and touching the x -axis at a distance of 3 units from the origin. If the circle C has an intercept of length 6 3 on y -axis, 2026Let the line x - y = 4 intersect the circle C: (x-4)^2 + (y+3)^2 = 9 at the points Q and R . If P( , ) is a point on C such that PQ = PR , then (6 + 8 )^2 is equal to __________. 2026Let the centre of the circle x^2 + y^2 + 2gx + 2fy + 25 = 0 be in the first quadrant and lie on the line 2x - y = 4 . Let the area of an equilateral triangle inscribed in the circl 2026Let P be a moving point on the circle x^2 + y^2 - 6x - 8y + 21 = 0 . Then, the maximum distance of P from the vertex of the parabola x^2 + 6x + y + 13 = 0 is equal to: 2026Suppose that two chords, drawn from the point (1, 2) on the circle x^2 + y^2 + x - 3y = 0 are bisected by the y -axis. If the other ends of these chords are R and S , and the mid p 2026Let a circle pass through the origin and its centre be the point of intersection of two mutually perpendicular lines x + (k-1)y + 3 = 0 and 2x + k^2 y - 4 = 0 . If the line x - y + 2026 Full Circle list All Highly selective Backlog Qs for JEE Main PYQs