I've just finished my pure h/work but the final question has me a bit baffled because in lectures we've only been dealing with parabols where the focus is like (a,0) and the directrix is just y=k where k is a real number. However, for this question we've to find the eqt of the parabola whose focus is at the point (1,1) and whose directrix has the eqt x + y = 0(adsbygoogle = window.adsbygoogle || []).push({});

I've drawn it out so that I've chosen an arbitrary point (x', y') and then worked out the distance between this point and the focus to be the square root of (x' - 1)^2 + (y' - 1)^2

For working out the distance between the point and the directrix I've got the modulus of (x' + y')/sqrt2

I've then set these two equal to each other by the definition of the parabola and got x^2 + y^2 -2xy -4x- 4y +4=0 as the eqt of the parabola. Can someone confirm if hi is is correct or not?

The second part of the question is that if the line ax + by+ c =0 is a tangent to the parabola, then show that the line bx + ay +c=0 is also one of its tangents. I'm really not sure how to go about this one. I thought maybe you could differentiate the eqt of the parabola and then diferentiate the eqts of the tangents and work from there, but it's going pear-sharped. Can anyone point me in the right direction? Thanks!

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# Eqt of the parabola question

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