Home
Class 12
MATHS
The ellipse (x^(2))/(a^(2))+(y^(2))/(b^...

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 .

Text Solution

Verified by Experts

The correct Answer is:
`a=5sqrt2;b=4sqrt2`
Promotional Banner

Topper's Solved these Questions

  • MISCELLANEOUS EXAMPLES

    CHHAYA PUBLICATION|Exercise WBHS ARCHIVE 2017 (UNIT-5)|6 Videos

  • MISCELLANEOUS EXAMPLES

    CHHAYA PUBLICATION|Exercise WBHS ARCHIVE 2017 (UNIT-6)|2 Videos

  • MISCELLANEOUS EXAMPLES

    CHHAYA PUBLICATION|Exercise WBHS ARCHIVE 2017 (UNIT-3)|16 Videos

  • METHOD OF SUBSTITUTION

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Examination (Assertion-Reason Type)|2 Videos

  • ORDER AND DEGREE OF DIFFERENTIAL EQUATION

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Examination (E Assertion - Reasion Type )|2 Videos

Similar Questions

Explore conceptually related problems

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

The hyperbola (x^(2))/(a^(2)) - (y^(2))/(b^(2)) = 1 passes throught the point of intersection of the lines x - 3sqrt(5)y =0 and sqrt(5)x - 2y = 13 and the length of its latus rectum is (4)/(5) . Find the coordinates of its foci.

The ellipse x^2/a^2+y^2/b^2=1 passes through the point of intersection of the lines 7x+13y=87and 5x-8y+7=0and the length of its latus rectum is (32sqrt2)/5 units.Find the values of a and b.

The hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2)) = 1 passes through the point of intersection of the lines x + y = 3, 2x - 3y = 1. and its eccentricity is sqrt(3) , show that its length of latus rectum is 2sqrt(14) .

If the ellipse x^2/a^2+y^2/b^2=1 passes through the intersecting points of two straight lines 7x + 13y -87=0 and 5x -8y + 7 = 0 and the'length of its latus rectum is (32sqrt2)/5 then find the value of a and b and also find its eccentricity

If the parabola y^(2) = 4 ax passes through the point of intersection of the straight lines 3x + y + 5 = 0 and x + 3y - 1 = 0 , find the coordinates of its focus and the length of its latus rectum .

Prove that, The line 5x + 4y = 0 passes through the point of intersection of straight lines x+2y-10 = 0, 2x + y =-5

Find the equation of the line passing through the point of intersection of the lines 4x + 7y - 3 = 0 " and " 2x - 3y + 1 = 0 that has equal intercepts on the axes.

If the straight line (x)/(a) + (y)/(b) = 1 is parallel to the line 4x + 3y = 6 and passes through the point of intersection of the lines 2x - y - 1 = 0 and 3x - 4y + 6 = 0 ,find the values of a and b .

If the hyperbola x^2/a^2-y^2/b^2=1 passes through the interesecting point of two straight lines x=3sqrt5 y and sqrt5x-2y=13 and the length of latus rectum is 4/3 unit,the find the co-ordinate of its focus.