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<img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/CEN_CG_C04_S01_073_S01.png" width="80%"> <br> Variable point on the line `2x+y-4` is `P(t,4-2t),t in R`. <br> Equation of chord of contact `x^(2)+y^(2)=1` w.r.t. point P is <br> `tx +(4-2t)y=1` <br> or `(4y-1)+t(x-2y)=0` <br> This is the equation of family of straight lines which are concurrent at point of intersection of lines `4y-1=0` and `x-2y=0`. <br> Therefore , line are concurrent at `Q (1//2,1//4)` Transcript

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00:00 - 00:59 | hello student in this question we are given that tangents are drawn to the circle which is Axis square + Y square is equal to 1 from an arbitrary point on the line which is 2x + Y - 4 is equal to zero then we have to prove that corresponding codes of contact passes through a fixed point and we have to find that point also ok means means we have a circle ok we have a circle like this and this is X square + Y square is equal to 1 and we also have a line we also have a line like this is the line which is 2x + Y - 4 is equal to zero and we have a variable point |

01:00 - 01:59 | P on this line it say this is the point P and co-ordinate of this point will be what this is variable means you can you can place any variable point on this equation suppose if x will be t-x will be the reason why will be what we will be 24 - 2T write checks will be it then why will be 4 - 2T right so we can say variable point is this if we will try to if you will try to draw tangent from this point to the circle then this will be the tangent drawn tangent is this and another tangents can be drawn this right we can draw out these two tangent |

02:00 - 02:59 | then the chord of contact of the tangent will be the chord of contact of these two tangent will be this right and the equation of the tangent will be w x Into X 1st + Y into Y1 is 4 - 2T is equal to 1 why because there is a concept if you have a circle X square + Y square is equal to 1 and you have a point P which is X X1 Y1 and if you want to draw a tangent from this point to the circle like this then tangent of then chord of contact of these two tangent will be XX oneplus yy1 educole 2 |

03:00 - 03:59 | because this is what ok one square this is one square ok so we will apply this comes we have applied this concept here now we got this for Y minus 2 Y is equal to minus 1 minus 1 is equal to zero right or you can say it will be common X - 2y this can be written as 4 Y - 1 is equal to zero write if you see this this is nothing but our family of a straight line this is nothing but a family of a straight line which passes through a fixed point which is assessed through a fixed point |

04:00 - 04:59 | that point is the intersection point of this and this line in there is a line for Y minus 1 is equal to zero and another line is x minus 2 Y is equal to zero from here you can save Y is equal to 1 by 4 right hand from here x is equal to 2 wife are you can save x is equal to 2 into why is 1 by 4 mens half so you can say tax will be half so this code this code of contact will passes through a fixed point which is 1 by 4 One by Two always ok and this is what we have to prove thank you |

**Standard equation of circle**

**General Equation of Circle When the circle passes through the origin.**

**General Equation of Circle When the circle touch x axis and y axis .**

**General Equation of Circle When the circle touches both the axis.**

**Important points to remember**

**Find the Equation; radius; center of the circle and its x intercept and y intercept ?**

**Theorem:- Prove that the equation `x^2+y^2+2gx+2fy+c=0` always represent a circle whose centre is `(-g;-f)` and radius `sqrt(g^2+f^2-c)`**

**Diameter form of the circle**

**Parametric form of circle**

**Equation of a circle passing through 3 points**