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Hi, The family of straight lines is used when we need to represent large number of lines representing a particular condition....
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Hello Student If you consider two triangles which are formed by the diagonal of the trapezium. In both the triangle base will be parallel to mid point of sides and both sides are also parallel hence...
Hello Student, Please post the full question again. Your question is not so clear. Thanks,...
Since none of the lines are perpendicular therefore it is not a right angled triangle. now find the intersection points of x+y=0, 3x+y-4=0, x+3y-4=0, we get (2,-2),(-2,2) & (1,1) let A(2,-2)...
Sir,Actually they are asking on which line x1,y1 lies :) ?
Please check the question and post it once again x 2 +y 2 =4 is not a eqn of ellipse...
Hello Student. Please find the solutionx+y+1=0 and x+y-1 are two parallel lines and distance between them is mod|\frac{1-(-1)}{\sqrt{2}} |So distabce between them is 2/root2 = root2So our req line us...
hey I have a simpler and unique solution Use family of circles passing through two points and then put third point to get the constant The required circle’s equation will be S + k L = 0 where S is...
length of AP and AQ is as these are diagonals of square with side 1. Since AP and AQ are diagonals of square ASPF and ABQR respectively Also, due to hexagon property, angle between adjacent sides is ,...
Definition says that the asymptotes of rectangluar hyperbolar are cordinate axis i.e x and y axis By the definition of asymptotes hyperbola meets it at infinity. So rectangular hyperbola intersects...
Shortest focal chord is chord perpendicular to axis and passing through focus. for above parabola focus is (8,0) End points of focus will be (8,16) and (8, -16) ( Get y by putting x=8 iin parabola...
Hello Student, Please find the solution Here you can use the concept of family of lines The equation of the line passing through the inersection of lines x-y+1=0 and 2x-3y+5=0 can be assumed as Now...
Let us first solve for end points of the chord by finding points of intersection of chord and parabola: It is also interesting to note Let’s now call the slope of tangents at these two points...
A few results will help solving this problem Here, a,b,c are sides of the triangle. s is the semi-radius and r is the in-radius. Using these equations and given condition, we get 3s=4c which gives...
Hello Student, Please find the proof of this: Let us draw (construct) the straight line GH passing through thepoint C parallel to the triangle side AB. Such a line does exist due to postulate 1 of the...
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Let y=mx + c be the equation of chord Homogenize the equation of curve 3x 2 -y 2 -2x+4y=0 by putting 1= (y-mx)/c Equation becomes 3x 2 -y 2 -2x(y-mx)/c+4y(y-mx)/c=0 Homogenization gives the equation...
A (1,5) B (2,3) C (4,4) AB= √5 units BC=√5 units AC= √10 units Hence given triangle is right angled triangle ( AB2 + BC2 = AC2) at B Orthocenter is B only CIrcumcenter for rt...
A (1,5) B (2,3) C (4,4) AB= √5 units BC=√5 units AC= √10 units Hence given triangle is right angled triangle ( AB 2 + BC 2 = AC 2 ) at B Orthocenter is B only CIrcumcenter for rt...
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