Question

+ ht angled triangle What point on the v-axis Is equiusdino -- 0 - ) ! 0) The points A (03), B(-2, a) and C(-1, 4) are the vertices of a right anol at A, find the value of a. (m) The centre of a circle is (2a - 1, 3a + 1) and it passes through the point (-3 the value (s) of u if a diameter of the circle is of length 20 units. (1 18. Find the area of the triangle for show that these points are col 19. Find the area of the quadril (5,-2) and (-3,-1). 20. The coordinates of A, B and int (-3,-1). Find

JEE/Engineering Exams

Maths

Solution

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diameter ( =20 ) units ( Rightarrow ) radicus ( =10 ) unils Cevsre of cirle ( =(2 alpha-1,3 alpha+1) ) Equation of circle, ( (x-2 alpha+1)^{2}+(y-3 x-1)^{2}=(10)^{2} ) : Cirle pases through the point (-3,-1) ( Rightarrow(-3-2 x+1)^{2}+(-1-3 x-1)^{2}=100 ) ( Rightarrow quad(-2-2 alpha)^{2}+(-2-3 alpha)^{2}=100 ) ( Rightarrow(2+2 alpha)^{2}+(2+3 alpha)^{2}=100 ) ( Rightarrow quad 4 x^{2}+4+8 alpha+9 alpha^{2}+4+12 alpha=100 ) ( Rightarrow 13 alpha^{2}+20 alpha-92=0 ) ( Rightarrow quad 13 x^{2}-26 x+462-92=0 ) ( Rightarrow quad mid 3 x(alpha-2)+46(x-2)=0 ) ( Rightarrow quad alpha=-frac{46}{13}, 2 )