Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET201824 Apr 2018Morning ShiftMathematicsCircleActual

If the shortest distance from (2,-14) to the circle x^2+y^2+6 x+4 y-12=0 is d and the length of the tangent drawn from the same point to the circle is l , then d+l =

Options

  1. A13
  2. B2 5
  3. C12
  4. D5

Correct answer

B. 2 5

Step-by-step solution

Given circle, x^2+y^2+6 x+4 y-12=0 Here, centre is O(-3,-2) and radius = 9+4+12 = 25 =5 Shortest distance of the point P(2,-14) to the circle is circle is aligned A P & =d A P & =O P-O A (O A & =R) O P & = (-3-2)^2+(-2+14)^2 & = 25+144 = 169 =13 A P & =13-5=8=d aligned Length of tangent from the point P(2,-14) is aligned & = (2)^2+(-14)^2+6 2+4(-14)-12 & = 4+196+12-56-12 & = 144 =12=1 aligned So, required d+l = 8+12 = 20 =2 5 .

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