Half Yearly Conics Questions (1 Viewer)

[kevda1st]

I couldnt do these locus questions...please help

the ones i circled in red.

 

[SparkyZ]

For the first part, A hyperbola is called a hyperbola if its asymtotes meet at right angles. Also its eccentricity is root(2).

For the second part, I would assume you need to draw the diagram and use the rules of concyclic polygons.

 

[azureus88]

[maths]P(cp,\frac{c}{p})[/maths]

[maths]Q(cq,\frac{c}{q})\Rightarrow (\frac{cp}{2},\frac{2c}{p})[/maths]

The coordinates of midpoint M is given by:

[maths]x=\frac{cp+\frac{cp}{2}}{2}=\frac{3cp}{4}[/maths]

[maths]y=\frac{\frac{c}{p}+\frac{2c}{p}}{2}=\frac{3c}{2p}[/maths]

[maths]xy=(\frac{3cp}{4})(\frac{3c}{2p})=\frac{9c^2}{8}=d^2[/maths] which is in form of parabola

For the other question, use the fact that angle in semi-circle=90 degrees by using gradient formula

 

[kevda1st]

For the first part, A hyperbola is called a hyperbola if its asymtotes meet at right angles. Also its eccentricity is root(2).

For the second part, I would assume you need to draw the diagram and use the rules of concyclic polygons.

no shit. Im asking HOW you do it. Not what a hyperbola is

 

[SparkyZ]

If you knew what the definition of a Rectangular was, you wouldn't have asked our help to prove it, good thing azureus88 kindly posted the full solution for you, I just thought you would be smart enough to figure it out from what I said.