The monomial - ax & # 179; is about X, y, and the coefficient is 9, then a=______

The monomial - ax & # 179; is about X, y, and the coefficient is 9, then a=______

The coefficients include the preceding symbols
So - a = 9
a=-9

The number factor in the monomial of an algebraic expression is called its coefficient. What does it mean in simple terms?

The numerical part (including the symbol) in front of the letter is the coefficient

The line L passing through point a (0,3) and circle x ^ 2 + y ^ 2 = 1 intersect at two points a and B, and the triangle AOB has the largest area. The equation for finding L is given

Why two "A's"? Isn't the one in front?
Let the linear l equation be: Y-3 = KX, that is: kx-y + 3 = 0
The distance from the center of the circle to the straight line d = 3 / √ (K & # 178; + 1), radius r = 1
Ψ (| ab | / 2) &# 178; = R & # 178; - D & # 178; = 1 - 9 / (K & # 178; + 1) = (K & # 178; - 8) / (K & # 178; + 1) (Pythagorean theorem)
∴|AB|/2=√[ (k²-8) / (k²+1) ]
∴S△AOB
= D×|AB|/2
= [ 3/√(k²+1) ] × √[ (k²-8) / (k²+1) ]
= [3√(k²-8)] / (k²+1)
= [3√(k²-8)] / (k²- 8 + 9)
=3 / [√ (K & # 178; - 8) + 9 / √ (K & # 178; - 8)] (divide up and down the fraction by √ (K & # 178; - 8))
≤3/(2√9)
=1/2
If and only if √ (K & # 178; - 8) = 9 / √ (K & # 178; - 8), that is, k = ± √ 17, the equal sign holds
The linear l equation is: ± √ 17x - y + 3 = 0

Through a point P (3,1) outside the circle x ^ 2 + y ^ 2 = 4, make a straight line L intersecting at two points a and B. if the triangle AOB has the largest area, find the equation of the straight line L

The center of circle x ^ 2 + y ^ 2 = 4 is O (0,0), radius r = 2, let ∠ AOB = α, then s Δ AOB = 1 / 2 * r & # 178; sin α ≤ 1 / 2R & # 178; = 2, namely α = 90 & # 186; when s gets the maximum, take the midpoint of AB as m, then om ⊥ AB, and OM = √ 2 / 2R = √ 2, that is, the distance from O to line L is √ 2, then the slope of L exists, let K, then the equation of L is Y-1