Q69.If the tangent at (1, 7) to the curve x2 = y −6 touch the circle x2 + y2 + 16x + 12y + c = 0 then the value of c is: (1) 95 (2) 195 (3) 185 (4) 85
What This Question Tests
This question combines finding the equation of a tangent to a parabola and then using the condition that this tangent also touches a given circle, specifically that the distance from the circle's center to the tangent equals the radius.
Concepts Tested
Formulas Used
Equation of tangent to y=f(x) at (x1, y1): y - y1 = f'(x1)(x - x1)
Distance from center to tangent = radius for a circle
(x-h)^2 + (y-k)^2 = r^2
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📋 Question Details
- Chapter
- Circles
- Topic
- Tangents to curves and circles
- Year
- 2018
- Shift
- 08 Apr
- Q Number
- Q69
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 11: Conic Sections (for parabola), Class 11 Mathematics Ch 10: Straight Lines (for tangent), Class 12 Mathematics Ch 6: Applications of Derivatives (for tangent)
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