TextBook Solutions for Nagaland Board Class 11 Mathematics Chapter 11 Conic Section

The ellipse x²+ 4y²= 4 is inscribed in a rectangle aligned with the coordinate axes, which in turn is inscribed in another ellipse that passes through the point (4, 0). Then the equation of the ellipse is

• x²+ 16y²= 16 

• x²+ 12y²= 16 

• 4x²+ 48y²= 48 

• 4x²+ 64y²= 48

A focus of an ellipse is at the origin. The directrix is the line x = 4 and the eccentricity is 1/2. Then the length of the semi−major axis is 

• 8/3

• 2/3

• 5/3

• 4/3

A parabola has the origin as its focus and the line x = 2 as the directrix. Then the vertex of the parabola is at 

• (0, 2)

• (1, 0)

• (0,1)

• (2,0)

Consider a family of circles which are passing through the point (-1, 1) and are tangent to x-axis. If (h, K) are the co-ordinates of the centre of the circles, then the set of values of k is given by the interva

• 0 < k < 1/2

• k ≥ 1/2

• – 1/2 ≤ k ≤ 1/2

• k ≤ ½

The differential equation of all circles passing through the origin and having their centres on the x-axis is

The normal to a curve at P(x, y) meets the x-axis at G. If the distance of G from the origin is twice the abscissa of P, then the curve is a

• ellipse

• parabola

• circle

• hyperbola

For the Hyperbola  which of the following remains constant when α varies?

• Eccentricity

• Directrix

• Abscissae of vertices

• Abscissae of foci

The equation of a tangent to the parabola y² = 8x is y = x + 2. The point on this line from which the other tangent to the parabola is perpendicular to the given tangent is

• (−1, 1)

• (0, 2)

• (2, 4)

• (−2, 0)

The locus of the vertices of the family of parabolas 

In an ellipse, the distance between its foci is 6 and minor axis is 8. Then its eccentricity is

• 3/5

• 1/5

• 2/5

• 4/5