Home
Class 12
MATHS
Show that the equation 5x^(2) + 9y^(2) ...

Show that the equation `5x^(2) + 9y^(2) - 10 x + 90 y + 185 = 0 ` repesents an ellipse. Find length of latus rectum

Text Solution

Verified by Experts

The correct Answer is:
The length of its latus rectum `2*(b^(2))/(a) = 2 * (5)/(3) = (10)/(3)` unit
Promotional Banner

Topper's Solved these Questions

  • ELLIPSE

    CHHAYA PUBLICATION|Exercise M . C . Q|20 Videos
  • ELLIPSE

    CHHAYA PUBLICATION|Exercise Very Short Answer Type Qustions|33 Videos
  • DIRECTION COSINES AND DIRECTION RATIOS

    CHHAYA PUBLICATION|Exercise Assertion-Reason Type|2 Videos
  • GENERAL SOLUTIONS OF TRIGNOMETRIC EQUATIONS

    CHHAYA PUBLICATION|Exercise Assertion-Reason Type-|2 Videos

Similar Questions

Explore conceptually related problems

Show that the equation 5x^(2) + 9y^(2) - 10 x + 90 y + 185 = 0 repesents an ellipse. Find eccentricity

Show that the equation 5x^(2) + 9y^(2) - 10 x + 90 y + 185 = 0 represents an ellipse. Find the co-ordinates of it's center

Show that the equation 5x^(2) + 9y ^(2) - 10 x + 90 y + 185 = 0 represents an ellipse and find the equations of the directrices of this ellipse .

y^2+2y-x+5=0 represents a parabola. Find equation of latus rectum.

The equation y^(2) + 4x + 4y + k = 0 represents a parabola whose latus rectum is _

Find the coordinates of foci of the ellipse 5 x^(2) + 9y ^(2) - 10x + 90 y + 185 = 0

Find the coordinates of the vertices of the ellipse 5 x^(2) + 9y ^(2) - 10x + 90 y + 185 = 0

The ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 passes through the point of intersection of the lines 7x + 13 y - 87 = 0 and 5x - 8y + 7 = 0 and its length of latus rectum is (32sqrt(2))/(5) , find a and b .

If theta is a variable parameter , show that the equations x=(1)/(4)(3-cosec^(2)theta),y = 2 + cot theta represent the equation of a parabola. Find the coordinates of vertex , focus and the length of latus rectum of the parabola.

Taking major and minor axes as x and y - axes respectively , find the equation of the ellipse whose length of latus rectum is (18)/(5) unit and the coordinates of one focus are (4,0)