If the intercepts made by tangent, normal to a rectangular `x^2-y^2 =a^2` with x-axis are `a_1,a_2` and with y-axis are `b_1, b_2` then `a_1,a_2 + b_1b_2=`

If the line a x+b y=2 is a normal to the circle x^2+y^2-4x-4y=0 and a tangent to the circle x^2+y^2=1 , then a and b are

If the area of the circle is A_1 and the area of the regular pentagon inscribed in the circle is A_2, then find the ratio (A_1)/(A_2)dot

The tangents and normal at a point on (x^(2))/(a^(2))-(y^(2))/(b^(2)) =1 cut the y-axis A and B. Then the circle on AB as diameter passes through

Find the number of all three elements subsets of the set {a_1, a_2, a_3, a_n} which contain a_3dot

If same force is acting on two masses m_1 and m_2 and the accelerations of two bodies are a_1 and a_2 respectively, then

Prove that the area bounded by the circle x^2+y^2=a^2 and the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 is equal to the area of another ellipse having semi-axis a-b and a ,a > b .

If the equation of the locus of a point equidistant from the points (a_1, b_1) and (a_2, b_2) is (a_1-a_2)x+(b_1-b_2)y+c=0 , then the value of c is

Let vec a=a_1 hat i+a_2 hat j+a_3 hat k , vec b=b_1 hat i+b_2 hat j+b_3 hat ka n d vec c=c_1 hat i+c_2 hat j+c_3 hat k be three non-zero vectors such that vec c is a unit vector perpendicular to both vec aa n d vec b . If the angle between aa n db is pi/6, then prove that |(a_1 a_2a_3)(b_1b_2b_3)(c_1c_2c_3)|=1/4(a1 2+a2 2+a3 2)(b1 2+b2 2+b3 2)

Let vec a = a_1 hat i + a_2 hat j+ a_3 hat k;vec b = b_1 hat i+ b_2 hat j+ b_3 hat k ; vec c= c_1hat i + c_2 hat j+ c_3 hat k be three non-zero vectors such that vec c is a unit vector perpendicular to both vec a & vec b . If the angle between vec a and vec b is pi/6 , then |(a_1,b_1,c_1),(a_2,b_2,c_2),(a_3,b_3,c_3)|^2=

Let vec a=a_1 hat i+a_2 hat j+a_3 hat k , vec b=b_1 hat i+b_2 hat j+b_3 hat ka n d vec c=c_1 hat i+c_2 hat j+c_3 hat k be three nonzero vectors such that vec c is a unit vector perpendicular to both vec aa n d vec bdot If the angle between vec aa n d vec b is pi//6 , then the value of |a_1b_1c_1a_2b_2c_2a_3b_3c_3| is a. 0 b. 1 c. 1/4(a_1 2+a2 2+a3 2)(b1 2+b2 2+b3 2) d. 3/4(a1 2+a2 2+a3 2)(b1 2+b2 2+b3 2)