Q70.Let P be a point on the parabola x2 = 4y. If the distance of P from the center of the circle x2 + y2 + 6x + 8 = 0 is minimum, then the equation of the tangent to the parabola at P is (1) x + y + 1 = 0 (2) x + 4y −2 = 0 (3) x + 2y = 0 (4) x −y + 3 = 0
What This Question Tests
This question integrates concepts from parabolas (point on parabola, tangent) and circles (center, distance) along with calculus (minimizing distance using differentiation), making it a multi-concept and challenging problem.
Concepts Tested
Formulas Used
Distance formula = sqrt((x2-x1)^2 + (y2-y1)^2)
Equation of tangent to y^2=4ax at (x1,y1) is yy1=2a(x+x1)
Equation of tangent to x^2=4ay at (x1,y1) is xx1=2a(y+y1)
📚 NCERT Sections This Tests
2.1 — Two Charges 5 × 10–8 C And –3 × 10–8 C Are Located 16 Cm Apart. At
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2.1 Two charges 5 × 10–8 C and –3 × 10–8 C are located 16 cm apart. At what point(s) on the line joining the two charges is the electric potential zero? Take the potential at infinity to be zero.
9.8 — A Beam Of Light Converges At A Point P. Now A Lens Is Placed In The
Physics Class 12 · Chapter 9
9.8 A beam of light converges at a point P. Now a lens is placed in the path of the convergent beam 12cm from P. At what point does the beam converge if the lens is (a) a convex lens of focal length 20cm, and (b) a concave lens of focal length 16cm?
9.15 — Apply Mirror Equation And The Condition:
Physics Class 12 · Chapter 9
9.15 Apply mirror equation and the condition: (a) f < 0 (concave mirror); u < 0 (object on left) (b) f > 0; u < 0 (c) f > 0 (convex mirror) and u < 0 (d) f < 0 (concave mirror); f < u < 0 to deduce the desired result.
📋 Question Details
- Chapter
- Parabola
- Topic
- Tangent to parabola
- Year
- 2018
- Shift
- 16 Apr Online
- Q Number
- Q70
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 11: Conic Sections
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