Q71.A triangle is formed by the tangents at the point (2, 2) on the curves y2 = 2x and x2 + y2 = 4x, and the line x + y + 2 = 0. If r is the radius of its circumcircle, then r2 is equal to
What This Question Tests
This multi-concept question requires finding tangents to two different curves at the same point, determining the vertices of a triangle formed by these tangents and a given line, and then calculating the circumradius of that triangle. It is calculation-intensive and demands strong coordinate geometry skills.
Concepts Tested
Formulas Used
Equation of tangent to y²=4ax at (x₁,y₁): yy₁ = 2a(x+x₁)
Equation of tangent to circle x²+y²+2gx+2fy+c=0 at (x₁,y₁): xx₁+yy₁+g(x+x₁)+f(y+y₁)+c=0
Distance formula
Circumradius formula R = abc/(4Δ)
📚 NCERT Sections This Tests
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12.7 The radius of the innermost electron orbit of a hydrogen atom is 5.3×10–11 m. What are the radii of the n = 2 and n =3 orbits?
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📋 Question Details
- Chapter
- Straight Lines
- Topic
- Tangents to curves and circumcircle of a triangle
- Year
- 2023
- Shift
- 29 Jan Shift 2
- Q Number
- Q71
- Type
- Numerical
- NCERT Ref
- Class 11 Mathematics Ch 10: Straight Lines; Class 11 Mathematics Ch 11: Conic Sections
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