Maths-
General
Easy
Question
The sum of distances of any point on the ellipse 3 x2 + 4y2 = 24 from its foci is
- 8
- 4
- 16
- none of these
Hint:
The sum of the distances to any point on the ellipse (x,y) from the two foci (c,0) and (-c,0) is a constant. That constant will be 2a. If we let d1 and d2 bet the distances from the foci to the point, then d1 + d2 = 2a.
![](https://mycourses.turito.com/brokenfile.php#/136371/user/draft/778580321/download.png)
The correct answer is: 4 ![square root of 2](data:image/png;base64,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)
Given : ![3 x squared space plus space 4 y squared space equals space 24](data:image/png;base64,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)
Dividing both sides by 24, we get
![rightwards double arrow fraction numerator 3 x squared over denominator 24 end fraction space plus space fraction numerator 4 y squared over denominator 24 end fraction space equals space 1
rightwards double arrow space x squared over 8 space plus space y squared over 6 space equals space 1
C o m p a r i n g space f r o m space g e n e r a l space f o r m space x squared over a squared space plus space y squared over b squared space equals 1
rightwards double arrow a space equals space square root of 8 space space a n d space b space equals space square root of 6](data:image/png;base64,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)
The sum of the distances to any point on the ellipse (x,y) from the two foci (c,0) and (-c,0) is a constant. That constant will be 2a. If we let d1 and d2 bet the distances from the foci to the point, then d1 + d2 = 2a.
d1 + d2 = 2a
d1 + d2 = 2![square root of 8](data:image/png;base64,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)
d1 + d2 = 4![square root of 2](data:image/png;base64,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)
Thus, the sum of distances of any point on the ellipse 3 x2 + 4y2 = 24 from its foci is 4
.
Related Questions to study
Maths-
The equations x = a
represent
The equations x = a
represent
Maths-General
Maths-
The equations x = a cos q, y = b sin q, 0 ≤ q < 2 p, a ≠ b, represent
The equations x = a cos q, y = b sin q, 0 ≤ q < 2 p, a ≠ b, represent
Maths-General
Maths-
The line y = 2x + c touches the ellipse
if c is equal to
The line y = 2x + c touches the ellipse
if c is equal to
Maths-General
Maths-
The eccentricity of the conic 3x2 + 4y2 = 24 is
The eccentricity of the conic 3x2 + 4y2 = 24 is
Maths-General
Maths-
The equation of the ellipse whose focus is (1, -1). directrix x – y – 3 = 0 and eccentricity
is
The equation of the ellipse whose focus is (1, -1). directrix x – y – 3 = 0 and eccentricity
is
Maths-General
Maths-
The equation ax2 + 2hxy + by2 + 2gx + 2fy + c = 0 represents an ellipse if
The equation ax2 + 2hxy + by2 + 2gx + 2fy + c = 0 represents an ellipse if
Maths-General
Maths-
On a new year day every student of a class sends a card to every other student. The postman delivers 600 cards. The number of students in the class are :
On a new year day every student of a class sends a card to every other student. The postman delivers 600 cards. The number of students in the class are :
Maths-General
Maths-
A tangent to the ellipse x2 + 4y2 = 4 meets the ellipse x2 + 2y2 = 6 at P and Q. The angle between the tangents at P and Q of the ellipse x2 + 2y2 = 6 is
A tangent to the ellipse x2 + 4y2 = 4 meets the ellipse x2 + 2y2 = 6 at P and Q. The angle between the tangents at P and Q of the ellipse x2 + 2y2 = 6 is
Maths-General
Maths-
An ellipse has OB as a semi – minor axis, F, F' are its foci and the angle FBF' is a right angle. Then the eccentricity of the ellipse is
An ellipse has OB as a semi – minor axis, F, F' are its foci and the angle FBF' is a right angle. Then the eccentricity of the ellipse is
Maths-General
General
The equation of the tangents drawn at the ends of the major axis of the ellipse 9x2 + 5y2 – 30y = 0 is
The equation of the tangents drawn at the ends of the major axis of the ellipse 9x2 + 5y2 – 30y = 0 is
GeneralGeneral
Maths-
For the ellipse 3x2 + 4y2 – 6x + 8y – 5 = 0
For the ellipse 3x2 + 4y2 – 6x + 8y – 5 = 0
Maths-General
Maths-
If S’ and S are the foci of the ellipse
and P (x, y) be a point on it, then the value of SP + S’P is
If S’ and S are the foci of the ellipse
and P (x, y) be a point on it, then the value of SP + S’P is
Maths-General
Maths-
The eccentricity of the curve represented by the equation x2 + 2y2 – 2x + 3y + 2 = 0 is
The eccentricity of the curve represented by the equation x2 + 2y2 – 2x + 3y + 2 = 0 is
Maths-General
Maths-
The foci of the ellipse 25 (x + 1)2 + 9 (y + 2)2 = 225 are
The foci of the ellipse 25 (x + 1)2 + 9 (y + 2)2 = 225 are
Maths-General
Maths-
The eccentricity of the ellipse 9x2 + 5y2 – 30y = 0 is
The eccentricity of the ellipse 9x2 + 5y2 – 30y = 0 is
Maths-General