Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET202615 April 2026Evening ShiftMathematicsCircleActual

The angle between the tangents drawn from the origin to the circle (x-7)^2 + (y+1)^2 = 25 is

Options

  1. A45^
  2. B90^
  3. C60^
  4. D30^

Correct answer

B. 90^

Step-by-step solution

The equation of the circle is (x-7)^2 + (y+1)^2 = 25 . The center of the circle is C(7, -1) and its radius is r = 5 . Let the tangents be drawn from the origin O(0, 0) and the angle between them be 2 . The distance between the origin and the center of the circle is OC = (7-0)^2 + (-1-0)^2 = 50 = 5 2 . From the right-angled triangle formed by the origin, the center, and the point of contact, we have = r OC . = 5 5 2 = 1 2 = 45^ The angle between the tangents is 2 = 90^ .

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 MHT CET PYQs