Q86.Let a tangent to the curve 9๐ฅ2 + 16๐ฆ2 = 144 intersect the coordinate axes at the points ๐ด and ๐ต. Then, the minimum length of the line segment ๐ด๐ต is ______
What This Question Tests
This question requires finding the equation of a tangent to an ellipse, determining the intercepts it makes with the coordinate axes, and then minimizing the length of the segment connecting these intercepts, typically using parametric form and AM-GM inequality.
Concepts Tested
Formulas Used
x^2/a^2 + y^2/b^2 = 1
xx_0/a^2 + yy_0/b^2 = 1
Distance = sqrt((x_2-x_1)^2 + (y_2-y_1)^2)
a^2tan^2\theta + b^2cot^2\theta \ge 2ab
๐ NCERT Sections This Tests
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.
9.8 โ A Beam Of Light Converges At A Point P. Now A Lens Is Placed In The
Physics Class 12 ยท 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 โ Apply Mirror Equation And The Condition:
Physics Class 12 ยท 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.
๐ Question Details
- Chapter
- Ellipse
- Topic
- Tangent to an ellipse, Minimum length
- Year
- 2023
- Shift
- 24 Jan Shift 1
- Q Number
- Q86
- Type
- Numerical
- NCERT Ref
- Class 11 Mathematics Ch 11: Conic Sections
More from this Chapter
Q81.A focus of an ellipse is at the origin. The directrix is the line x = 4 and the eccentricity is 1/2. Then the length of the semi-major axis is (1) 8 (2) 2 3 3 (3) 4 (4) 5 3 3
Q69.Equation of the ellipse whose axes are the axes of coordinates and which passes through the point (โ3, 1) and has eccentricity is โ25 (1) 5x2 + 3y2 โ48 = 0 (2) 3x2 + 5y2 โ15 = 0 (3) 5x2 + 3y2 โ32 = 0 (4) 3x2 + 5y2 โ32 = 0 Q70.$$ \lim _{x \rightarrow 2}\left(\frac{\sqrt{1-\cos \{2(x-2)\}}}{x-2}\right) (1) equals โ2 (2) equals โโ2 (3) equals 1 (4) does not exist โ2
Q69.If P1 and P2 are two points on the ellipse x24 + y2 = 1 at which the tangents are parallel to the chord joining the points (0, 1) and (2, 0), then the distance between P1 and P2 is (1) 2โ2 (2) โ5 (3) 2โ3 (4) โ10
Q72.An ellipse is drawn by taking a diameter of the circle (x โ1)2 + y2 = 1 as its semiminor axis and a diameter of the circle x2 + (y โ2)2 = 4 as its semi-major axis. If the centre of the ellipse is the origin and its axes are the coordinate axes, then the equation of the ellipse is (1) 4x2 + y2 = 4 (2) x2 + 4y2 = 8 (3) 4x2 + y2 = 8 (4) x2 + 4y2 = 16