Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET202018 Sep 2020Evening ShiftMathematicsCircleActual

The length of the chord intercepted by the circle (x^2+y^2-6 x+8 y-5=0 ) on the line (2 x-y=5 ) is equal to units

Options

  1. A10
  2. B12
  3. C7
  4. D8

Correct answer

A. 10

Step-by-step solution

Centre (=(3,-4) ) ( Radius = 9+16+5 = 30 ) (d= ) Perpendicular distance from ((3,-4) ) to the chord (2 x-y-5=0 ) ( aligned d & = |2(3)-(-4)-5| 4+1 d & = |6+4-5| 5 d & = 5 length of chord & =2 r^2-d^2 =2 30-5 & =2 5=10 units aligned ) Hence, option (a) is correct.

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