The equation of common tangents to the parabola y2 8x and...

Transcript

00:01 Hello students we are going to write here in this particular question we are given here y square is 8 x if i write here for this so what would be equation if i write here so basically if i write here for this this must be our parabola if i write here for this and equation of tangent to parabola is always y is equals to mx plus we need to write here a divided by m so this is y squared y squared is equal to eight x so we need to write according to y square is equal to four a x right so if i compare four a is equal to eight where a is equal to two so equation is y is equals to mx plus 2 divided by m so basically if i write here for this in the next case we need to write here for this this is our equation number 1 now we need to write here this is our hyperbola which we are given 3x square 3 x square minus y square is equals to we need to write here for this 3 and x square minus y squared divided by three is one so basically if i write here for this equation of tangent in this particular case is equation of tangent is y is equals to mx plus minus we need to write here m square minus a square so so this is m square minus b square so here if i write here x square minus y squared divided by b square is 1 so if i compare a is 1 and b is we need to write here for this so b must be we need to write here plus under root of 3 and a is plus minus 1 so basically b square is 3 so basically if i write here this must be equation number 2 so if i compare we need to write here for this equation 1 and 2 what we are going to get here this must be 1 divided by 1 so we are going to write here we are comparing both equation 1 divided by 1 and m divided by m and 2 divided by m and under root of m square minus 3 so definitely this is under root of m square minus 3 is equivalent to 2 divided by m we need to write here for this so basically if i write here let's square both sides this is m square minus 3 is 4 divided by m square so this can be written as m square minus 4 divided by m square minus 3 is equal to 0 so basically if i write here this is m raised to power 4 minus 3 m square we need to write here for this 3 m square minus 4 is equal to 0 so basically if i write here for this this is m to power 4 minus 4m squared plus 4 m square plus m square minus 4 is equal to 0 as this is compared to a x square plus bx plus c is equal to 0 and we have applied factorization method where we have we have break our middle terms such like this that the sum of this middle term would be equal to second term and the multiplication of this must be equivalent to a multiple so definitely if i write here for this this must be written as m square m square minus 4 plus m square minus 4 is equal to 0 so basically if i write here for this m square plus 1 m square plus 1 we need to write here for this and m square minus 4 so so m value is plus minus 2.

04:23 So we are going to put our m value into y is equal to mx plus if i write here 2 divided by m so y is equal to plus minus 2 x plus 2 divided by we need to write here for this plus minus 2 so basically if i write here for this, so in the first case, let's say we take m value as plus 2.

04:50 So let's say m value is plus 2.

04:52 So this can be y is equal to 2x plus 1.

04:56 And if i write here for this, this can be written as 2x minus y plus 1 is equal to 0...