Q87.Let the tangent to the curve ๐ฅ2 + 2๐ฅ- 4๐ฆ+ 9 = 0 at the point ๐1, 3 on it meet the ๐ฆ- axis at ๐ด. Let the line passing through ๐ and parallel to the line ๐ฅ- 3๐ฆ= 6 meet the parabola ๐ฆ2 = 4๐ฅ at ๐ต. If ๐ต lies on the line 2๐ฅ- 3๐ฆ= 8, then ๐ด๐ต2 is equal to _______ .
What This Question Tests
This multi-concept question involves finding the tangent to a parabola-like curve, determining coordinates of points based on line equations and parallelism, and finally calculating the square of the distance between two points.
Concepts Tested
Formulas Used
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)
Distance formula
๐ NCERT Sections This Tests
2.3 โ Two Charges 2 Mc And โ2 Mc Are Placed At Points A And B 6 Cm
Physics Class 11 ยท Chapter 2
2.3 Two charges 2 mC and โ2 mC are placed at points A and B 6 cm apart. (a) Identify an equipotential surface of the system. (b) What is the direction of the electric field at every point on this surface?
2.1 โ Two Charges 5 ร 10โ8 C And โ3 ร 10โ8 C Are Located 16 Cm Apart. At
Physics Class 11 ยท Chapter 2
2.1 Two charges 5 ร 10โ8 C and โ3 ร 10โ8 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 โ A Parallel Plate Capacitor With Air Between The Plates Has A
Physics Class 11 ยท Chapter 2
2.5 A parallel plate capacitor with air between the plates has a capacitance of 8 pF (1pF = 10โ12 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?
๐ Question Details
- Chapter
- Coordinate Geometry
- Topic
- Tangents to parabolas and general coordinate geometry
- Year
- 2023
- Shift
- 06 Apr Shift 1
- Q Number
- Q87
- Type
- Numerical
- NCERT Ref
- Class 11 Mathematics Ch 11: Conic Sections | Class 11 Mathematics Ch 10: Straight Lines
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Q68.A light ray emerging from the point source placed at P(1, 3) is reflected at a point Q in the axis of x. If the reflected ray passes through the point R (6, 7), then the abscissa of Q is: (1) 1 (2) 3 (3) 7 (4) 5 2 2
Q76.If two vertices of an equilateral triangle are A(โa, 0) and B(a, 0), a > 0, and the third vertex C lies above x- axis then the equation of the circumcircle of โณABC is : (1) 3x2 + 3y2 โ2โ3ay = 3a2 (2) 3x2 + 3y2 โ2ay = 3a2 (3) x2 + y2 โ2ay = a2 (4) x2 + y2 โโ3ay = a2