1.

A cruve is respresented by C=21x^(2)-6xy+29y^(2)+6x-58y-151=0 The lengths of axes are

Answer»

`6,2 sqrt(6)`
`5,2sqrt(5)`
`4,4sqrt(5)`
none of these

Solution :`24X^(2)-6xy+29y+6x-58y-151=0`
`2(x-3y+3)^(2)+2(3x+y-1)^(2)=180`
or `((x-3y+3)^(2))/(60)+((3x+y-1)^(2))/(90)=1`
or `((x-3y+3)/(sqrt(1+3^(2))sqrt(6)))^(2)+((3x+y-1)/(3sqrt(1+3^(2))))=1`
Thus, C is an ellipse whose lengths of AXES are `6,2sqrt(6)`.
The minor and the major axes are `x-3y+3=0 and 3x+y-1=0`, respectively.
Their point of intersection gives the CENTER of the center of the conic. THEREFORE, Center `-=(o,1)`


Discussion

No Comment Found

Related InterviewSolutions