Q72.If the tangent to the conic, y −6 = x2 at (2, 10) touches the circle, x2 + y2 + 8x −2y = k (for some fixed k ) at a point (α, β); then (α, β) is (1) (−717 , 176 ) (2) (−817 , 172 ) (3) (−617 , 1017 ) (4) (−417 , 171 )
What This Question Tests
This question requires finding the equation of a tangent to a parabola, then using this line's property of being tangent to a circle to find the point of contact on the circle.
Concepts Tested
Formulas Used
Tangent to y=ax²+b at (x1,y1) is y-y1 = 2ax1(x-x1)
Distance from center to tangent = radius
Equation of normal at point of contact
📚 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.
2.5 — 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?
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.
📋 Question Details
- Chapter
- Parabola
- Topic
- Tangents to parabola and circle
- Year
- 2015
- Shift
- 10 Apr Online
- Q Number
- Q72
- Type
- Multi concept
- NCERT Ref
- Class 11 Mathematics Ch 11: Conic Sections
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