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Dear Student, For three co-ordinates of the triangle are given then, the coordinates of incentre of the triangle is given by (x,y) = (ax 1 +bx 2 +cx 3 /(a+b+c) , ay 1 +by 2 +cy 3 /(a+b+c)), where a ,...

we have many equations let the common normal intersect P1 at (x1,y1) and P2 at (x2,y2) 1) we have 2) we have 3) By equating the nomal slope at points, and the slope of the line we get eliminate any...

Dear Student, Follow the given steps. 1. Find the radius and center of the given circle. 2. Find the points of intersection of line with the circle. 3. Find the perpendicular distance of line from the...

the center radius form of the equation is the fomate (x-h) 2 +(y-k) 2 =r 2 ,with the center being at the point (h,k)and the radius being “r” this form of equation is helpful, since you easily find...

Use this formula to find ∂ first abc + 2fgh – af 2 – bg 2 – ch 2 = 0 There after we can use angle between 2 SL’s formula tanθ=|m1-m2 / 1+m1m2|.

The answer for your question is 22.5 0 all the best for your bright future bye /........................................

Let x+iy=root of 8+3i (x+iy) 2 =8+3i x 2 -y 2 +2xyi=8+3i On comparing, x2-y2=8 and 2xy=3 ie x=3/(2y) 9/(4y 2 ) – y 2 =8 Solve and get the values of x and y z=x+iy

let then which yields hence the two lines are as follows these are parallel lines When the lines are given by ax+by+c 1 =0 ax+by+c 2 =0 the distance between them can be expressed as so in this case

Dear Student. The distance between the incenter andcircumcenteris sqrt(R(R-2r)) , where R is thecircumradiusand r is theinradius, a result known as theEuler triangle formula. Thanks.

Dear Abhishek, you can use the formula of area of triangle which is A=1/2 of |x1 y1 1| |x2 y2 1| |x3 y3 1|

Dear Student, Correction is there, On solving the equation, we get – m1/m2. So negative sign is missing over there. Thanks.

Dear Student, If any curve strike on y = x line, its reflection is juct x replaced by y and y replaced by x. Thanks.

length of focal chord of parabola y2=4ax is given by formula = 4a cosec^2 θ tanθ → slope Now u can find slope from given info

this has a good collection http://www.askiitians.com/iit-jee-3d-geometry/direction-cosines-of-a-line/

It’s simple Lets say L1 is y=mx Then as chords are equal the perpendicular distance from the center of the circle should also be same center is (1/2,-3/2) so we have (by equating the...

Look at the figure attached Here ABC is an isocelous triangle with angle A= angle B CM and BN are the angle bisectors So now we observe tri(BMC) and tri(BNC) 1) BC = BC 2) ang(MBC) = ang(NCB) 3)...

OK so first we solve for the lines whihc gives the two lines as and now plotting them on the coordinate axes, it’s easy to see by symmetry that the center of circle would lie on x- axis and...

Dear Student, Striaght line is the locus of point such that it is always collinear with the given twoi fixed points. Parametric method is a way of expressing the function (or coordinate of point) in...

this is a Right angled triangle and its Orthocentre is at side containing 90 degree so 0,0 is the answer as it pas through origin !

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Dear Student, Calcuate y from given equation of line and put it in the equation of parabola. Noiw since the line touches that means the D = 0 for the quadratic equaiton. Hence you will get k = 1....

we can modify the equation of the line as as a>0 the x and y intercepts are a and 1/(a 2 +1) hence the area of the triangle formed is we need to maximize the area wrt a so and hence solving that we...

As shown in the figure due to the symmetry in parabolas the shortest distance AB will be perpendicular to the line x=y so we just need to find the coordinates of A tangent at A will be parallel to...

Keep in the mind of the above figure, also I wont write the triangle symbol given: area (AOB) = p = ax/2 and area (DOC) = q = by/2 proof: area (ABCD) = area(ABD) + area(ABC) – area(AOB) + area...

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