Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET202319 May 2023Morning ShiftMathematicsCircleActual

If P (2,3) and Q (-1,2) are conjugate points with respect to the circle x^2+y^2+2 g x+3 y-2=0 , then the radius of the circle is

Options

  1. A19 6
  2. B3 21 2
  3. C3 3 2
  4. D35 2

Correct answer

B. 3 21 2

Step-by-step solution

Since P(2,3) and Q(-1,2) are conjugate point w.r.t. the circle x^2+y^2+2 g x+3 y-2=0 Hence both the points lie on the polar of the other point Let P (x₁, y₁ )=P(2,3) Q (x₂, y₂ )=Q(-1,2) Hence aligned & (x₁ x₂ )+ (y₁ y₂ )+2 g ( x₁+x₂ 2 )+3 ( y₁+y₂ 2 )-2=0 & g=- 19 2 aligned Since radius r= g^2+f^2-c r= (- 19 2 )^2+ (- 3 2 )^2-(-2) = 3 21 2

Practice Circle on Quantrex Academy →

More from Circle

A circle touches both the coordinate axes and the straight line L 4 x +3 y -6=0 in the first quadrant. If this circle lies below the line L =0 , then the equation of that circle is 2025If the smallest circle through the points of intersection of x^2+y^2=a^2 and x +y =p, 0 < p < a is x^2+y^2-a^2+ (x +y -p)=0 then = 2025If the lines 3 x-4 y+4=0 and 6 x-8 y-7=0 are the tangents to the same circle, then the area of that circle (in sq.units) is 2025Circles are drawn through the point (2,0) to cut intercepts of length 5 units on the X -axis. If their centre lie in the first quadrant, then their equation is 2025The circles x^2+y^2-2 x-4 y-4=0 and x^2+y^2+2 x+4 y-11=0 2025If the line 4 x-3 y+7=0 touches the circle x^2+y^2-6 x+4 y-12=0 at ( , ) , then +2 = 2025The slope of the common tangent drawn to the circles x^2+y^2-4 x+12 y-216=0 and x^2+y^2+6 x-12 y+36=0 is 2025If r₁ and r₂ are radii of two circles touching all the four circles (x r)^2+(y r)^2=r^2 , then r₁+r₂ r = 2025 Full Circle list All AP EAMCET PYQs