What will be the value of angle between the curves x² - y² = 2a² and x² + y² = 4a²?
In easy words, we verify π/3 by full calculation: use standard identity, substitute, simplify step by step to reach π/3.
Ref: NCERT Mathematics Class XI and XII
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If the normal to the ellipse x² + 3y² = 12 at the point be inclined at 60° to the major axis, then at what angle does th
Think of it like this: complete solution: write formula, plug data, do arithmetic. Final value matches 30°. Simple and accurate.
Ref: NCERT Mathematics Class XI — Coordinate Geometry
What will be the co-ordinates of the foot of the normal to the parabola y² = 3x which is perpendicular to the line y = 2
From the definition, complete solution: write formula, plug data, do arithmetic. Final value matches (3/16, 3/4). Simple and accurate.
Ref: NCERT Mathematics Class XI — Coordinate Geometry
What will be the co-ordinates of the foot of the normal to the parabola y² = 5x that makes an angle 45° with the x axis?
Look at it this way: after simplifying, (5/4, -5/2) is left. The method is simple: formula → substitution → calculation → answer.
Ref: NCERT Mathematics Class XI — Coordinate Geometry
If the curves x2/a + y2/b = 1 and x2/c + y2/d = 1 intersect at right angles, then which one is the correct relation?
The trick is we verify a – b = c – d by full calculation: use standard identity, substitute, simplify step by step to reach a – b = c – d.
Ref: NCERT Mathematics Class XI — Sets, Relations and Functions
What will be the equation of the normal to the parabola y2 = 3x which is perpendicular to the line y = 2x + 4?
Let's break it down: after simplifying, 16x + 32y = 27 is left. The method is simple: formula → substitution → calculation → answer.
Ref: NCERT Mathematics Class XI — Coordinate Geometry
What will be the equation of the normal to the parabola y² = 5x that makes an angle 45° with the x axis?
Notice that we verify 4(x – y) = 15 by full calculation: use standard identity, substitute, simplify step by step to reach 4(x – y) = 15.
Ref: NCERT Mathematics Class XI — Coordinate Geometry
What are the direction ratios of the line of intersection of the planes x = 3z + 4 and y = 2z - 3?
From the definition, using formula we get 〈3, 2, 1〉. Calculation gives this directly, check steps: apply rule, substitute values, simplify to get 〈3, 2, 1〉.
Ref: NCERT Mathematics Class XII — Vectors and 3D Geometry
The locus of a point P(x, y, z) which moves in such a way that z = 7 is a
Let's break it down: complete solution: write formula, plug data, do arithmetic. Final value matches plane parallel to xy - plane. Simple and accurate.
Ref: NCERT Mathematics Class XII — Vectors and 3D Geometry
Find distance between the lines L₁ and L₂ whose vector equations are r = ; i + j + k + ; ( 3 i - j );and; r = 4 i- k + (
We know that using formula we get 2. Calculation gives this directly, check steps: apply rule, substitute values, simplify to get 2.
Ref: NCERT Mathematics Class XII — Vectors and 3D Geometry
The value of k such that the line x-4/1=y-2/1=z-k/2 is lying on the plane 2x - 4y + z = 7 will be?
Think of it like this: solving fully: apply relevant formula, put numbers, compute. Result comes as 7. Easy verification shows it satisfies condition.
Ref: NCERT Mathematics Class XI and XII
Equation of a plane parallel to xz plane at unit distance is
Applying the basic concept, complete solution: write formula, plug data, do arithmetic. Final value matches y = 1. Simple and accurate.
Ref: NCERT Mathematics Class XII — Vectors and 3D Geometry
