Perhaps you have covered the following result:
The family of conics passing through is
The following is a 'multiple-option correct' question..
If the straight line 3x+4y=24 intersects the axes at A and B and the straight line 4x+3y=24 at C and D, then the points A,B,C and D lie on:
(a) a Circle
(b) a Parabola
(c) an Ellipse
(d) a Hyperbola
My attempt:
I got the points A,B,C and D by solving the given equations.. which are (0,6) (0,8) (6,0) (8,0).
I am definitely sure that the option (A) is right..
Because i got a clear equation of a circle with centre at (7,7) and its radius being √50..
But how do i proceed for the other conics.... Kindly help
In such a case:
(a) You have proved that the four points lie on a circle.
(b) The four points lie on that is on a pair of parallel lines (degenerated parabola).
(c) A circle is a particular case of an elipse.
(d) The four points lie on that is, on a pair of non parallel lines (degenerated hyperbola).
Hello, animesh271094!
. .
. . . Right!
If we are allowed "tipped" conics, all four answers are correct.
The general quadratic equation is:
. .
Substitute the four points . . .
Subtract: .
Substitute into [2]: .
Subtract: .
Substitute into [6]: .
From [4] and [8]: .
. . and [7] becomes: .
The quadratic equation becomes:
. .
If , we have the circle that you found.
Otherwise, the conics are all rotated clockwise.
The discriminant is: .
Select values for and and you can have any of the conic curves.