OP Malhotra Class-11 Ellipse S.Chand ISC Maths Solution Chapter-24. Step by step Solutions of OP Malhotra S.Chand ISC Class-11 Mathematics with Exe-24, With Chapter Test. Visit official Website CISCE for detail information about ISC Board Class-12 Mathematics.
OP Malhotra Class-11 Ellipse S.Chand ISC Maths Solution
| Class: | 11th |
| Subject: | Mathematics |
| Chapter : | Ch-24 Ellipse of Section -A |
| Board | ISC |
| Writer | OP Malhotra |
| Publications | S.Chand Publications 2020-21 |
–: Select Topics :-
OP Malhotra Class-11 Ellipse S.Chand ISC Maths Solution
Ellipse
An ellipse is the set of all points in a plane such that the sum of whose distances from two fixed points is constant.
or
An ellipse is the set of all points in the plane whose distances from a fixed point in the plane bears a constant ratio, less than to their distance from a fixed point in the plane. The fixed point is called focus, the fixed line a directrix and the constant ratio(e) the eccentricity of the ellipse. We have two standard forms of ellipse
Definition of Ellipse
An ellipse if we speak in terms of locus, it is the set of all points on a XY-plane, whose distance from two fixed points (known as foci) adds up to a constant value.
A circle is also an ellipse, where the foci are at the same point, which is the center of the circle.
Ellipse is defined by its two-axis along x and y-axis: Major axis and Minor Axis. The major axis is the longest diameter of the ellipse, going through the center from one end to the other, at the broad part of ellipse. Whereas the minor axis is the shortest diameter of ellipse, crossing through the center at the narrowest part.
Eccentricity of the Ellipse
The ratio of distances from the center of the ellipse from either focus to either of the vertices of the ellipse is defined as the eccentricity of the ellipse.
The eccentricity of ellipse, e = c/a
Since c ≤ a the eccentricity is always greater than 1 in the case of an ellipse.
Ellipse Equation
When the centre of the ellipse is at the origin (0,0) and the foci are on x-axis and y-axis, then we can easily derive the ellipse equation.
The equation of the ellipse is given by;
x2/a2 + y2/b2 = 1
Ellipse Formula
As we know, an ellipse is a closed-shape structure in a two-dimensional plane. Hence, it covers a region in a 2D plane. So, this bounded region of the ellipse is its area. The shape of the ellipse is different from circle, hence the formula for its area will also be different.
Area of Ellipse
Area of the circle is calculated based on its radius, but the area of the ellipse depends on the length of the minor axis and major axis.
Area of the circle = πr2
And,
Area of the ellipse = π x Major Axis x Minor Axis
| Area of the ellipse = π.a.b |
where a and b are the length of the minor axis and major axis.
Exe-24
OP Malhotra Class-11 Ellipse S.Chand ISC Maths Solution
Page 24-12 to 24-14
Question 1:
Find the eccentricity of the ellipse of which the major axis is double the minor axis.
Question 2:
……………………
……………………
…………………….
Question 27:
Find the eccentricity of the ellipse of minor axis i26, if the line segment joining the force …………………………. find the equation of ellipse.
Chapter Test
OP Malhotra Class-11 Ellipse S.Chand ISC Maths Solution
Page 24-17
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