Q71.Let the tangent to the parabola y2 = 12x at the point (3, α) be perpendicular to the line 2x + 2y = 3 . Then the square of distance of the point (6, −4) from the normal to the hyperbola α2x2 −9y2 = 9α2 at its point (α −1, α + 2) is equal to .............
What This Question Tests
This is a multi-concept question involving tangents and normals for both parabolas and hyperbolas, requiring calculation of slopes, equations of lines, and finally the distance between a point and a line.
Concepts Tested
Formulas Used
Tangent to y^2=4ax at (x1,y1): yy1 = 2a(x+x1)
Normal to x^2/a^2 - y^2/b^2 = 1 at (x1,y1): a^2x/x1 + b^2y/y1 = a^2+b^2
Distance formula
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📋 Question Details
- Chapter
- Applications of Derivatives
- Topic
- Tangent and normal to parabola and hyperbola
- Year
- 2023
- Shift
- 11 Apr Shift 2
- Q Number
- Q71
- Type
- Numerical
- NCERT Ref
- Class 12 Mathematics Ch 6: Application of Derivatives | Class 11 Mathematics Ch 11: Conic Sections
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