Q63.If m is the slope of a common tangent to the curves x2 16 + 9 = 1 and x2 + y2 = 12 , then 12m2 is equal to JEE Main 2022 (26 Jun Shift 2) JEE Main Previous Year Paper (1) 6 (2) 9 (3) 10 (4) 12
What This Question Tests
This question involves finding the slope of a common tangent to an ellipse and a circle by equating the conditions for a line to be tangent to both curves, and then solving for the slope 'm'.
Concepts Tested
Formulas Used
Tangent to x²/a² + y²/b² = 1 is y = mx ± sqrt(a²m² + b²)
Tangent to x² + y² = r² is y = mx ± r*sqrt(1 + m²)
📚 NCERT Sections This Tests
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?
9.23 — (A) At What Distance Should The Lens Be Held From The Card Sheet In
Physics Class 12 · Chapter 9
9.23 (a) At what distance should the lens be held from the card sheet in Exercise 9.22 in order to view the squares distinctly with the maximum possible magnifying power? (b) What is the magnification in this case? (c) Is the magnification equal to the magnifying power in this case? Explain.
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
- Coordinate Geometry
- Topic
- Common Tangents to Ellipse and Circle
- Year
- 2022
- Shift
- 26 Jun Shift 2
- Q Number
- Q63
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 11: Conic Sections
More from this Chapter
Q78.The perpendicular bisector of the line segment joining P(1, 4) and Q(k, 3) has y-intercept - 4. Then a possible value of k is (1) 1 (2) 2 (3) −2 (4) −4
Q72.The normal at (2, 23 ) to the ellipse, x216 + y23 = 1 touches a parabola, whose equation is (1) y2 = −104x (2) y2 = 14x (3) y2 = 26x (4) y2 = −14x sin(π cos2 x)
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(−a, 0) and B(a, 0), a > 0, and the third vertex C lies above x- axis then the equation of the circumcircle of △ABC is : (1) 3x2 + 3y2 −2√3ay = 3a2 (2) 3x2 + 3y2 −2ay = 3a2 (3) x2 + y2 −2ay = a2 (4) x2 + y2 −√3ay = a2