Q21.Let A and B be the two points of intersection of the line y + 5 = 0 and the mirror image of the parabola y2 = 4x with respect to the line x + y + 4 = 0. If d denotes the distance between A and B , and a denotes the area of △SAB, where S is the focus of the parabola y2 = 4x, then the value of (a + d) is -
What This Question Tests
This question is multi-conceptual, requiring calculation of the mirror image of a parabola, finding the intersection points of this new curve with a given line, then calculating distance and area based on these points and the parabola's focus.
Concepts Tested
Formulas Used
Image of (x,y) across ax+by+c=0: (x'-x)/a = (y'-y)/b = -2(ax+by+c)/(a^2+b^2)
Focus of y^2=4ax is (a,0)
Distance formula d = √((x₂-x₁)² + (y₂-y₁)²)
Area of triangle: 1/2 |x₁(y₂-y₃) + x₂(y₃-y₁) + x₃(y₁-y₂)|
📚 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?
9.15 — 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.
9.1 — A Small Candle, 2.5 Cm In Size Is Placed At 27 Cm In Front Of A Concave
Physics Class 12 · Chapter 9
9.1 A small candle, 2.5 cm in size is placed at 27 cm in front of a concave mirror of radius of curvature 36 cm. At what distance from the mirror should a screen be placed in order to obtain a sharp image? Describe the nature and size of the image. If the candle is moved closer to the mirror, how would the screen have to be moved?
📋 Question Details
- Chapter
- Parabola
- Topic
- Mirror image of a parabola, Intersection of line and parabola, Area of a triangle
- Year
- 2025
- Shift
- 28 Jan Shift 2
- Q Number
- Q21
- Type
- Numerical
- NCERT Ref
- Class 11 Mathematics Ch 11: Conic Sections; Class 11 Mathematics Ch 10: Straight Lines
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