Q87.Two tangent lines l1 and l2 are drawn from the point (2, 0) to the parabola 2y2 = −x. If the lines l1 and l2 are also tangent to the circle (x −5)2 + y2 = r, then 17r2 is equal to y2
What This Question Tests
This problem requires finding the equations of tangents to a parabola from an external point, and then applying the condition for these lines to be tangent to a given circle to determine the radius squared.
Concepts Tested
Formulas Used
Tangent to y^2 = 4ax is y = mx + a/m
Tangent to x^2 = 4ay is x = my - am^2
Distance from (x1, y1) to Ax+By+C=0 is |Ax1+By1+C|/sqrt(A^2+B^2)
📚 NCERT Sections This Tests
2.1 — Two Charges 5 × 10–8 C And –3 × 10–8 C Are Located 16 Cm Apart. At
Physics Class 11 · Chapter 2
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.
2.2 — A Regular Hexagon Of Side 10 Cm Has A Charge 5 Mc At Each Of Its
Physics Class 11 · Chapter 2
2.2 A regular hexagon of side 10 cm has a charge 5 mC at each of its vertices. Calculate the potential at the centre of the hexagon.
2.5 — A Parallel Plate Capacitor With Air Between The Plates Has A
Physics Class 11 · Chapter 2
2.5 A parallel plate capacitor with air between the plates has a capacitance of 8 pF (1pF = 10–12 F). What will be the capacitance if the distance between the plates is reduced by half, and the space between them is filled with a substance of dielectric constant 6?
📋 Question Details
- Chapter
- Parabola
- Topic
- Tangent to parabola and circle
- Year
- 2022
- Shift
- 28 Jul Shift 2
- Q Number
- Q87
- Type
- Numerical
- NCERT Ref
- Class 11 Mathematics Ch 11: Conic Sections (Parabola), Class 11 Mathematics Ch 11: Conic Sections (Circle)
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