Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET20224 Jul 2022Evening ShiftMathematicsCircleActual

The ratio of the largest and shortest distances from the point 2 , - 7 to the circle x 2 + y 2 - 14 x - 10 y - 151 = 0 is

Options

  1. A15 : 13
  2. B7 : 1
  3. C3 : 2
  4. D14 : 1

Correct answer

D. 14 : 1

Step-by-step solution

Given equation of circle, x 2 - 14 x + 49 + y 2 - 10 y + 25 - 74 - 151 = 0 On rearranging we get, x - 7 2 + y - 5 2 = 225 ⇒ x - 7 2 + y - 5 2 = 15 2 So, Centre = 7 , 5 and Radius = 15 units Now putting x = 2 & y = - 7 In the clrcle's equation, - 5 2 + - 12 2 - 225 < 0 So, 2 , - 7 lies inside the circle. Now distance from 2 , - 7 to 7 , 5 = x 2 - x 1 2 + y 2 - y 1 2 D = 7 - 2 2 + 5 - - 7 2 D = 5 2 + 12 2 = 13 Now shortest distance will be r - 13 = 15 - 13 = 2 And largest distance will be r + 13 = 15 +

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