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The lines ax + 2y + 1 = 0, bx + 3y + 1 = 0 and cx + 4y + 1 = 0 are concurrent if a, b, c are in G.P.
Concept: undefined >> undefined
Given the ellipse with equation 9x2 + 25y2 = 225, find the major and minor axes, eccentricity, foci and vertices.
Concept: undefined >> undefined
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Find the equation of the ellipse with foci at (± 5, 0) and x = `36/5` as one of the directrices.
Concept: undefined >> undefined
The equation of the circle in the first quadrant touching each coordinate axis at a distance of one unit from the origin is ______.
Concept: undefined >> undefined
The equation of the circle having centre (1, –2) and passing through the point of intersection of the lines 3x + y = 14 and 2x + 5y = 18 is ______.
Concept: undefined >> undefined
The equation of the ellipse whose centre is at the origin and the x-axis, the major axis, which passes through the points (–3, 1) and (2, –2) is ______.
Concept: undefined >> undefined
The equation of the circle which passes through the point (4, 5) and has its centre at (2, 2) is ______.
Concept: undefined >> undefined
If the lines 3x – 4y + 4 = 0 and 6x – 8y – 7 = 0 are tangents to a circle, then find the radius of the circle.
Concept: undefined >> undefined
Find the equation of a circle which touches both the axes and the line 3x – 4y + 8 = 0 and lies in the third quadrant.
Concept: undefined >> undefined
Find the distance between the directrices of the ellipse `x^2/36 + y^2/20` = 1
Concept: undefined >> undefined
The shortest distance from the point (2, –7) to the circle x2 + y2 – 14x – 10y – 151 = 0 is equal to 5.
Concept: undefined >> undefined
Draw appropriate Venn diagram for the following:
(A ∪ B)'
Concept: undefined >> undefined
Draw appropriate Venn diagram for the following:
A' ∩ B'
Concept: undefined >> undefined
Draw appropriate Venn diagram for the following:
(A ∩ B)'
Concept: undefined >> undefined
Draw appropriate Venn diagram for the following:
A' ∪ B'
Concept: undefined >> undefined
In a survey it was found that 21 people liked product A, 26 liked product B and 29 liked product C. If 14 people liked products A and B, 12 people liked products C and A, 14 people liked products B and C and 8 liked all the three products. Find how many liked product C only.
Concept: undefined >> undefined
Find the derivative of x2 – 2 at x = 10.
Concept: undefined >> undefined
Find the derivative of 99x at x = 100.
Concept: undefined >> undefined
Find the derivative of x at x = 1.
Concept: undefined >> undefined
For the function
f(x) = `x^100/100 + x^99/99 + ...+ x^2/2 + x + 1`
Prove that f'(1) = 100 f'(0)
Concept: undefined >> undefined
