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(1) <br> Any parabola whose axes whose axes is parallel to the x-axis will be of the from <br> `(y-a)^(2)=4b(x-c)` (1) <br> Now, lx+my=1 can be rewritten as <br> `y-a=-(l)/(m)(x-c)+(1-am-lc)/(m)` (2) <br> Equation (2) will touch (1) if <br> `(1-am-lc)/(m)=(b)/(-l//m)` <br> `or-(l)/(m)=(bm)/(1-am-lc)` <br> `orcl^(2)-bm^(2)+alm-l=0` (3) <br> But given that <br> `5l^(2)+6m^(2)-4lm+3l=0` (4) <br> Comparing (3) and (4), we get <br> `(c)/(5)=(-b)/(6)=(a)/(-4)=(-1)/(3)` <br> `orc=(-5)/(3),b=2,anda=(4)/(3)` <br> So, the parabola is <br> `(y-(4)/(3))^(2)=8(x+(5)/(3))` <br> whose focus is `(1//3,4//3)` and directrix is 3x+11=0.`Transcript

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00:00 - 00:59 | hello students the question is find the area of triangle whose vertex power 38 - 42 and so we have to find the area of triangle area of triangle is the formula is area of given by Delta equal to 1 by 2 X 1 X 2 X and Y 1 by 2 and search for ms111 is the formula of area of triangle so now here I put the value is given in question so sweet 1 X 1 is the value of 3 and X2 is the value of minus 4 |

01:00 - 01:59 | is the value of one by one which is equal to I take this one second numbers value so edit Y2 which is equal to 2 and finally y3 which is equal to is given by one of the value in this form now so Delta equal to 1 by 2 to the modulus value 3 X 2 x minus 4 x 5 survival in 822111 what is already given in the first grow and expand the destroyer and the column from this value is not comes in this so this |

02:00 - 02:59 | multiple 1 by 2 into 2 First row as column value with 3 into multiple this phone digit for values photo into 12 minus 1 into 1 is 18 and a first true value in multiple - 4 - 5 x + Y - 10 so now I multiple this so 1 by 2 into 3 into 2 - 11 - 8 into minus 4 -5 is answer is - 9 + 1 YouTube - 4 - |

03:00 - 03:59 | is -14 now 1 by 2 into 2 the value is 3 into 3 cube minus into minus plus so I put the values + 18 27 is valued 72 Som plus into minus minus 14 the answer is 61 divided by 2 is please answer so that we required area of triangle 1882 square unit so this is the answer of this question students thank you so much |