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9h
comment Find the equation of the locus of the mid-point between an elliptical point and its directrix
Thanks! One last question: why does $b=\frac{1}{2}$ (in $y=b\sin\theta = \frac{1}{2}\sin\theta$)? I thought, from the original equation, that $b^2=1$
9h
accepted Find the equation of the locus of the mid-point between an elliptical point and its directrix
9h
comment Find the equation of the locus of the mid-point between an elliptical point and its directrix
@user_of_math Thanks. By squaring them, I get: $(4x^2 -4 - 4\cos\theta) + (4y^2) = 1$. Which leads to: $4x^2 + 4y^2-4x+3=0$. But the answer has $-8x$ not $-4x$
9h
comment Find the equation of the locus of the mid-point between an elliptical point and its directrix
So the midpoints would be $\left(\frac{\pm \sqrt{1-4y^2} + 2}{2}, y\right)$?
9h
comment Find the equation of the locus of the mid-point between an elliptical point and its directrix
Why did you use these parameters: $x=\cos\theta, y=\frac{1}{2}\sin\theta$? Sorry - I'm having a slow day :)
9h
comment Find the equation of the locus of the mid-point between an elliptical point and its directrix
Okay, I understand how you got the midpoint coordinates - but how do I find the locus equation with that?
10h
asked Find the equation of the locus of the mid-point between an elliptical point and its directrix
11h
asked Find the x-coordinate as the chord of two points on a parabola touches the x-axis
14h
comment Finding the equations of the tangents to a circle with center $(3a,0)$
Thanks! Seems obvious now :)
14h
accepted Finding the equations of the tangents to a circle with center $(3a,0)$
14h
comment Finding the equations of the tangents to a circle with center $(3a,0)$
Let the hypothenuse (also the radius) be $4a$, and the angle 30; then the adjacent (the length of the tangent) must equal $a\sqrt3$ right?
14h
comment Finding the equations of the tangents to a circle with center $(3a,0)$
Just because $L$ touches the circle doesn't mean that $\triangle OLC$ is a right-angled triangle does it? I didn't think that $L$ or $M$ sat above the centre... I know that $\angle LOC = 30$...
14h
asked Finding the equations of the tangents to a circle with center $(3a,0)$
19h
accepted Prove that the locus of a point P is a circle
1d
comment Prove that the locus of a point P is a circle
Why does $|AP|^2 = 9|BP|^2$ rather than $|AP|=9|BP|$?
2d
comment Prove that the locus of a point P is a circle
Ah thank you, that seems much simpler. How about the last section of the question with point Q?
2d
asked Prove that the locus of a point P is a circle
Oct
21
accepted Find the equations of the two circles which pass through the point $(2,0)$ and have both the $y$-axis and the line $y-1=0$ as tangents
Oct
21
comment Find the equations of the two circles which pass through the point $(2,0)$ and have both the $y$-axis and the line $y-1=0$ as tangents
How did you get $r=\dfrac{|a|}{\sqrt{1^2+0^2}}$ and $r=\dfrac{|b-1|}{\sqrt{1^2+0^2}}$? If it's the pythagorean theorem, what are the other sides?
Oct
21
asked Find the equations of the two circles which pass through the point $(2,0)$ and have both the $y$-axis and the line $y-1=0$ as tangents