Question
The number of values of c such that the straight line y = 4x + c touches the curve 
+ y2 = 1 is
- 0
- 1
- 2
- infinite
The correct answer is: 2
Related Questions to study
If P(x, y), F1=(3,0), F2 = (– 3, 0)and16x2 + 25 y2 = 400, then P F1 + P F2 =
If P(x, y), F1=(3,0), F2 = (– 3, 0)and16x2 + 25 y2 = 400, then P F1 + P F2 =
Let P be a variable point on the ellipse 
+ 
= 1 with foci F1 and F2. If A is the area of the triangle PF1 F2, then the maximum value of A is-
Area of triangle with given vertices can be calculated using the matrix determimnant method.
Let P be a variable point on the ellipse + = 1 with foci F1 and F2. If A is the area of the triangle PF1 F2, then the maximum value of A is-
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The eccentricity of an ellipse, with its centre at the origin, is 
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standard equation of ellipse is
x2/a2+y2/b2=1
The eccentricity of an ellipse, with its centre at the origin, is . If one of the directrices is x = 4, then the equation of the ellipse is-
standard equation of ellipse is
x2/a2+y2/b2=1
The foci of the ellipse 
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– 
= 
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focus of ellispe = ae,0
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The equation of an ellipse, whose major axis = 8 and eccentricity = 1/2, is
Arrangement of the following ellipses in ascending order of the radii of their director circles
P) 4x2 + 9y2 = 36
Q) 3x2 + 4y2 = 12
R) 9x2 + 16y2 = 144
S) x2 + 2y2 = 4
the radius of director circle is equal to the length of semi major axis.
Arrangement of the following ellipses in ascending order of the radii of their director circles
P) 4x2 + 9y2 = 36
Q) 3x2 + 4y2 = 12
R) 9x2 + 16y2 = 144
S) x2 + 2y2 = 4
the radius of director circle is equal to the length of semi major axis.
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the distances of the points from a line can be calculated by using the distance formula.
If p and p' denote the lengths of the perpendicular from a focus and the centre of an ellipse with semi-major axis of length a, respectively, on a tangent to the ellipse and r denotes the focal distance of the point, then
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An ellipse and a hyperbola have the same centre “origin”, the same foci. The minor-axis of the one is the same as the conjugate axis of the other. If e1, e2 be their eccentricities respectively, then 
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P is a point on the ellipse . The in-radius of ΔPSS’ (S and S’ are focii), where its area is maximum.
in radius is the radius of the circle inscribed inside the triangle.
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in radius is the radius of the circle inscribed inside the triangle.
Equation of one of the common tangent of y2 = 4x and 
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a common tangent is a line that is a tangent to more than one curves..
Equation of one of the common tangent of y2 = 4x and is equal to-
a common tangent is a line that is a tangent to more than one curves..
If F1 and F2 are the feet of the perpendiculars from the foci S1 & S2 of an ellipse 
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If F1 and F2 are the feet of the perpendiculars from the foci S1 & S2 of an ellipse on the tangent at any point P on the ellipse, then (S1 F1). (S2 F2) is equal to-
selecting a point on the major axis provides an ease of calculation.
The number of real tangents that can be drawn to the ellipse 3x2 + 5y2 = 32 and 25x2 + 9y2 = 450 passing through (3 , 5) is
if a point lies inside, no real tangents can be drawn from the point on the curve. on the curve, then only 1 tangent and if outside, then 2 tangents can be drawn.
The number of real tangents that can be drawn to the ellipse 3x2 + 5y2 = 32 and 25x2 + 9y2 = 450 passing through (3 , 5) is
if a point lies inside, no real tangents can be drawn from the point on the curve. on the curve, then only 1 tangent and if outside, then 2 tangents can be drawn.
P is a variable point on the ellipse += 1 with AA' as the major axis. Then, the maximum value of the area of the triangle APA' is-wor
when we differentiate an expression, we get the critical points where either maxima or minima can exist.
P is a variable point on the ellipse += 1 with AA' as the major axis. Then, the maximum value of the area of the triangle APA' is-wor
when we differentiate an expression, we get the critical points where either maxima or minima can exist.
