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Let any tangent to the parabola `y^(2) = 8x` be `y = mx + (4)/(m)`. It also touches the circle `x^(2) + y^(2) = 8` <br> `therefore` Length of perpendicular from centre of the circle to the line = radius of the circle. <br> `rArr|(0-0+(4)/(m))/(sqrt(1+m^(2)))|=2sqrt(2)` <br> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/AAK_T4_MAT_C11_SLV_033_S01.png" width="80%"> <br> `((4)/(m))^(2) = 8 + 8m^(2)` <br> `m^(2) + m^(2) -2 = 0` <br> `(m^(2) + 2) (m^(2) -1) =0` <br> `m = pm 1` <br> `therefore` The common tangents are <br> `y = x + 4 and y = - x - 4` <br> Point of intersection of these tangents is `P(-4, 0)` Equation of chord of contact to the circle from `P(-4, 0)` is <br> `-4x + 0 = 8 rArr x + 2 = 0` <br> Equation of chord of contact of tangents to the parabola is <br> `0 = 4(x -4)` <br> `rArr x - 4 = 0` <br> Redrawing the figure formed by four lines, we require the area of the shaded region i.e., trapezium <br> Required area ` =(1)/(2) (AD + BC) xx MN` <br> `=(1)/(2) (4+16)xx6` <br> `=60` sq. units <br> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/AAK_T4_MAT_C11_SLV_033_S02.png" width="80%">Transcript

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00:00 - 00:59 | hello Siri question says find the area of the quadrilateral drawn to the circle x 8 and contact of tangent to the parabola ok we know that a standard form is look something like this is equal to 16 that he will be equal to for this the tangent is equal to Y = MX + c then the X and Y Y is equal why |

01:00 - 01:59 | is MX + for a circle the distance of the centre of the circle from the equal to radius circle as it 2000 and it is 22 Centre little bcs-040 and radius is equal to root therefore I can say that Mod of why will be 0 - 10 - 2 root 2 upon under root of coefficient of Y + Y square + x square by under root 1 + sin square is equal to I am so sorry I made a mistake dishoom equal to minus 4 by m |

02:00 - 02:59 | m is equal to 22 so I can solve square and square is equal to 8 x + sin square is equal to MC square into X square + Y square will be equal to is equal to 1 and the other possibility is equal to minus 2 but since MS real this is not possible if I am still be equal to an equal to Angle B equal to plus minus one I can get the now the equation of the tangent will be by = S minus x + 4 |

03:00 - 03:59 | OK so I will get that the point of the point P - 404 and tigers 2 - 3 x + 4 equal to now I can find the contact with inner circle using the on people's 20 to see the circle is equal to zero is equal to zero record of music portal contact replacing x square with a square with xx1 y square with yy1 X with X + 1 by 2 Y + Y + 1 by 2 and she will remain cox1 and Y1 presence what is the external point to a circle |

04:00 - 04:59 | are so as to from this we can say that people will represent the chord of contact of circle which will be in this case - 4 x + 20 equal to C is it that implies X equal to minus 2 upon x square x y z will be zero because I can write 16 X 16 Into X + 3 x minus 4 upon x is equal to s a |

05:00 - 05:59 | x + 4 and Y equal to minus y equal to X + 4 and Y + 1 is equal to plot a graph say it will look something like it will do something like this and the points will be this this this and this is a 4 and the sin is equal to minus 2 is the exact and this will be the why so now we can see that it is a trapezium and the area of trapezium is equal to sum of parallel sides that is let it be L1 and L2 So album plus L2 and the height BH so into edge at this distance BH area so I can say that |

06:00 - 06:59 | I have to find first L1 and L2 decided by cos x + 4 Allah to solve it with X and get this is this will be a comma Sunny -2 kam 2 and minus minus and this will be and aur Seth 1602 into the 16 - 24 - 641 finance |

07:00 - 07:59 | options are not given that the answer is 240 thank you |