The equation of the parabola whose focus is the point (0$$,$$0) and the tangent at the vertex is x−$$y+1=0$$ is

Question

The equation of the parabola whose focus is the point (0$$,$$0) and the tangent at the vertex is x−$$y+1=0$$ is

Infinity Learn · Accepted Answer

Tangent at the vertex is x−$$y+1=0-----(1)Therefore$$, the equation of the axis of the parabola is $$X+Y=0------(2)$$ Now, solving (1) and (2), we get A≡$$($$−$$1/2$$,$$1/2)$$ .  Therefore, Z is $$($$−$$1$$,$$1)$$. $$($$∵A is midpoint of $$OZ)$$ Now, the directrix is $$X-Y+K=0$$ But this passes through $$Z($$−$$1$$,$$1)$$. Therefore, $$K=0$$ So, the directrix is x−$$y+2=0Therefore$$, by definition, the equation of the parabola isgiven $$byOP=PM$$ or $$OP2=PM2x$$−$$y+222=x2+y2$$ or  $$(x$$−$$y+2)2=2x2+2y2$$ or  $$x2+y2+4$$−$$2xy+4x$$−$$4y=2x2+2y2$$ or  $$x2+y2+2xy$$−$$4x+4y$$−$$4=0$$

$The equation of the parabola whose focus is the point (0, 0) and the tangent at the vertex is x - y + 1 = 0 is$

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

The equation of the parabola whose focus is the point (0,0) and the tangent at the vertex is x−y+1=0 is

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

$The equation of the parabola whose focus is the point (0, 0) and the tangent at the vertex is x - y + 1 = 0 is$