Q89.If the area of the triangle formed by the x-axis, the normal and the tangent to the circle (x −2)2 + (y −3)2 = 25 at the point (5, 7) is A, then 24A is equal to _________.
What This Question Tests
This problem involves finding the equations of the tangent and normal to a circle at a given point, determining their intersections with the x-axis, and then calculating the area of the triangle formed.
Concepts Tested
Formulas Used
Slope of tangent m = - (x₁-h) / (y₁-k)
Equation of line y - y₁ = m(x - x₁)
Area of triangle = 1/2 * base * height
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📋 Question Details
- Chapter
- Circles
- Topic
- Tangent and Normal to a Circle
- Year
- 2021
- Shift
- 24 Feb Shift 2
- Q Number
- Q89
- Type
- Numerical
- NCERT Ref
- Class 11 Mathematics Ch 11: Conic Sections
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